SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                 --------------


                    Under the Securities Exchange Act of 1934

                                  SCHEDULE 13G
                                 Amendment No. 1

             INFORMATION STATEMENT PURSUANT TO RULES 13d-1 AND 13d-2
                    UNDER THE SECURITIES EXCHANGE ACT OF 1934




                       Network-1 Security Solutions, Inc.
                       ----------------------------------
                                (Name of Issuer)



                     Common Stock, par value $0.01 per share
                     ---------------------------------------
                         (Title of Class of Securities)



                                   64121N-10-9
                                   -----------
                                 (CUSIP Number)



                                December 30, 2003
                 ----------------------------------------------
             (Date of Event Which Requires Filing of this Statement)



Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

      |_|   Rule 13d-1(b)
      |X|  Rule 13d-1(c)
      |_|  Rule 13d-1(d)


                                   ---------



                                  SCHEDULE 13G

CUSIP No. 64121N-10-9
--------------------------------------------------------------------------------

1)  NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    First New York Securities L.L.C.
    13-3270745
--------------------------------------------------------------------------------
2)  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a) |_|
                                                              (b) |X|
--------------------------------------------------------------------------------
3)  SEC USE ONLY

--------------------------------------------------------------------------------
4)  CITIZENSHIP OR PLACE OF ORGANIZATION

    New York
--------------------------------------------------------------------------------
       NUMBER                5)     SOLE VOTING POWER
       OF
       SHARES                       566,700
       BENEFICIALLY         ----------------------------------------------------
       OWNED BY              6)     SHARED VOTING POWER
       EACH
       REPORTING                    None
       PERSON               ----------------------------------------------------
       WITH                  7)     SOLE DISPOSITIVE POWER

                                    566,700
                            ----------------------------------------------------
                             8)     SHARED DISPOSITIVE POWER

                                    None
--------------------------------------------------------------------------------
9)  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

    566,700
--------------------------------------------------------------------------------
10) CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

                                                                   |-|
--------------------------------------------------------------------------------
11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

    6.8%
--------------------------------------------------------------------------------
12) TYPE OF REPORTING PERSON

    BD
--------------------------------------------------------------------------------



                                  SCHEDULE 13G

CUSIP No. 64121N-10-9
--------------------------------------------------------------------------------

1)  NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    Jay Goldstein
    145-70-6756
--------------------------------------------------------------------------------
2)  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a) |_|
                                                              (b) |X|
--------------------------------------------------------------------------------
3)  SEC USE ONLY

--------------------------------------------------------------------------------
4)  CITIZENSHIP OR PLACE OF ORGANIZATION

    United States
--------------------------------------------------------------------------------
       NUMBER                 5)     SOLE VOTING POWER
       OF
       SHARES                        150,000
       BENEFICIALLY          ---------------------------------------------------
       OWNED BY               6)     SHARED VOTING POWER
       EACH
       REPORTING                     None
       PERSON                ---------------------------------------------------
       WITH                   7)     SOLE DISPOSITIVE POWER

                                     150,000
                             ---------------------------------------------------
                              8)     SHARED DISPOSITIVE POWER

                                     166,700
--------------------------------------------------------------------------------
9)  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

    316,700
--------------------------------------------------------------------------------
10) CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

                                                                   |-|
--------------------------------------------------------------------------------
11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

    3.8%
--------------------------------------------------------------------------------
12) TYPE OF REPORTING PERSON

    IN
--------------------------------------------------------------------------------



                                  SCHEDULE 13G

CUSIP No. 64121N-10-9
--------------------------------------------------------------------------------

1)  NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    Douglas Lipton
    266-86-3053
--------------------------------------------------------------------------------
2)  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a) |_|
                                                              (b) |X|
--------------------------------------------------------------------------------
3)  SEC USE ONLY

--------------------------------------------------------------------------------
4)  CITIZENSHIP OR PLACE OF ORGANIZATION

    United States
--------------------------------------------------------------------------------
       NUMBER                  5)     SOLE VOTING POWER
       OF
       SHARES                         82,200
       BENEFICIALLY           --------------------------------------------------
       OWNED BY                6)     SHARED VOTING POWER
       EACH
       REPORTING                      None
       PERSON                 --------------------------------------------------
       WITH                    7)     SOLE DISPOSITIVE POWER

                                      82,200
                              --------------------------------------------------
                               8)     SHARED DISPOSITIVE POWER

                                      400,000
--------------------------------------------------------------------------------
9)  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

    482,200
--------------------------------------------------------------------------------
10) CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

                                                                   |-|
--------------------------------------------------------------------------------
11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

    5.8%
--------------------------------------------------------------------------------
12) TYPE OF REPORTING PERSON

    IN
--------------------------------------------------------------------------------



                                  SCHEDULE 13G

CUSIP No. 64121N-10-9
--------------------------------------------------------------------------------

1)  NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    Michael Marvin
    101-62-0101
--------------------------------------------------------------------------------
2)  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a) |_|
                                                              (b) |X|
--------------------------------------------------------------------------------
3)  SEC USE ONLY

--------------------------------------------------------------------------------
4)  CITIZENSHIP OR PLACE OF ORGANIZATION

    United States
--------------------------------------------------------------------------------
       NUMBER                  5)     SOLE VOTING POWER
       OF
       SHARES                         50,000
       BENEFICIALLY           --------------------------------------------------
       OWNED BY                6)     SHARED VOTING POWER
       EACH
       REPORTING                      None
       PERSON                 --------------------------------------------------
       WITH                    7)     SOLE DISPOSITIVE POWER

                                      50,000
                              --------------------------------------------------
                               8)     SHARED DISPOSITIVE POWER

                                      None
--------------------------------------------------------------------------------
9)  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

    50,000
--------------------------------------------------------------------------------
10) CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

                                                                   |-|
--------------------------------------------------------------------------------
11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

    0.6%
--------------------------------------------------------------------------------
12) TYPE OF REPORTING PERSON

    IN
--------------------------------------------------------------------------------



                                  Schedule 13G
                                  ------------

Item 1(a).  Name of Issuer:

Network-1 Security Solutions, Inc.

Item 1(b).  Address of Issuer's Principal Executive Offices:

445 Park Avenue, Suite 1028
New York, NY  10022

Item 2(a).  Name of Person Filing:

(1) First New York Securities L.L.C. ("FNYS")

(2) Jay Goldstein. Mr. Goldstein is employed by and trades securities of the
issuer for the proprietary account of FNYS.

(3) Douglas Lipton. Mr. Goldstein is employed by and trades securities of the
issuer for the proprietary account of FNYS.

(4) Michael Marvin. Mr. Marvin is employed by FNYS.


Item 2(b).  Address of Principal Business Office or, if None, Residence:

(1)   First New York Securities L.L.C.: 850 Third Avenue, 17th Floor
                                        New York, NY 10022

(2)   Jay Goldstein:                    1326 Crossing Way
                                        Wayne, NJ 07470

(3)   Douglas Lipton:                   1225 Park Avenue - Apt. 2A
                                        New York, NY  10128

(4)   Michael Marvin:                   352 East 89th Street - Apt. D
                                        New York, NY  10128

Item 2(c).  Citizenship:

(1)   First New York Securities L.L.C.: New York

(2)   Jay Goldstein:                    United States

(3)   Douglas Lipton:                   United States

(4)   Michael Marvin:                   United States

Item 2(d).  Title of Class of Securities:

Common Stock, par value $.01 per share



Item 2(e).  CUSIP Number:

64121N-10-9

Item 3.     If this statement is filed pursuant to ss.ss. 240.13d-1(b), or
            240.13d-2(b) or (c), check whether the person filing is a:

            (a)   |_| Broker or Dealer Registered Under Section 15 of the Act
                      (15 U.S.C. 78o)

            (b)   |_| Bank as defined in section 3(a)(6) of the Act (15 U.S.C.
                      78c)

            (c)   |_| Insurance Company as defined in section 3(a)(19) of the
                      Act (15 U.S.C. 78c)

            (d)   |_| Investment Company registered under section 8 of the
                      Investment Company Act of 1940 (15 U.S.C. 80a-8)

            (e)   |_| Investment Adviser in accordance with ss.
                      240.13d-1(b)(1)(ii)(E)

            (f)   |_| Employee benefit plan or endowment fund in accordance with
                      ss. 240.13d-1(b)(1)(ii)(F)

            (g)   |_| Parent Holding Company or control person in accordance
                      with ss.240.13d-1(b)(ii)(G)

            (h)   |_| Savings Association as defined in ss.3(b) of the Federal
                      Deposit Insurance Act (12 U.S.C. 1813)

            (i)   |_| Church plan that is excluded from the definition of an
                      investment company under ss.3(c)(15) of the Investment
                      Company Act of 1940 (15 U.S.C. 80a-3)

            (j)   |_| Group, in accordance with ss.240.13d-1(b)(ii)(J)

Item 4.     Ownership.

            (a) Amount beneficially owned:(1)

                (1)   First New York Securities L.L.C.:   566,700

                (2)   Jay Goldstein:                      316,700

                (3)   Douglas Lipton:                     482,200

                (4)   Michael Marvin:                      50,000

            (b) Percent of class:

                (1)   First New York Securities L.L.C.:   6.8%

                (2)   Jay Goldstein:                      3.8%

                (3)   Douglas Lipton:                     5.8%

                (4)   Michael Marvin:                     0.6%


---------------------
1 Percentages based on 8,314,458 shares of Common Stock outstanding as reported
in the Issuer's Form 10-QSB for the quarter ended September 30, 2003.



            (c) Number of shares as to which such person has:

                  (i)   Sole power to vote or to direct the vote:

                        (1)   First New York Securities L.L.C.: 566,700

                        (2)   Jay Goldstein:                    150,000

                        (3)   Douglas Lipton:                    82,200(2)

                        (4)   Michael Marvin:                    50,000

                  (ii)  Shared power to vote or to direct the vote:

                        (1)   First New York Securities L.L.C.: 0

                        (2)   Jay Goldstein:                    0

                        (3)   Douglas Lipton:                   0

                        (4)   Michael Marvin:                   0

                  (iii) Sole power to dispose or to direct the disposition of:

                        (1)   First New York Securities L.L.C.: 566,700

                        (2)   Jay Goldstein:                    150,000

                        (3)   Douglas Lipton:                    82,200(2)

                        (4)   Michael Marvin:                    50,000

                   (iv) Shared power to dispose or to direct the disposition of:

                        (1)   First New York Securities L.L.C.:  0

                        (2)   Jay Goldstein:                    166,700(3)

                        (3)   Douglas Lipton:                   400,000(3)

                        (4)   Michael Marvin:                   0

Item 5.     Ownership of Five Percent or Less of a Class.

Not Applicable.

Item 6.     Ownership of More than Five Percent on Behalf of Another Person.

Not Applicable.

Item 7.     Identification and Classification of the Subsidiary Which
            Acquired the Security Being Reported on by the Parent Holding
            Company.

Not Applicable.


---------------------
2 Includes 32,200 shares owned by Mr. Lipton's wife, as to which Mr. Lipton
disclaims beneficial ownership.

3 Shares owned by First New York Securities L.L.C. as to which the reporting
person may be deemed to share dispositive power.



Item 8.     Identification and Classification of Members of the Group.

See Item 2(a) above.

Item 9.     Notice of Dissolution of Group.

Not Applicable.

Item 10.    Certification.

            By signing below I certify that, to the best of my knowledge and
belief, the securities referred to above were not acquired and are not held for
the purpose of or with the effect of changing or influencing the control of the
issuer of the securities and were not acquired and are not held in connection
with or as a participant in any transaction having that purpose or effect.




                                    SIGNATURE
                                    ---------


         After reasonable inquiry and to the best knowledge and belief of the
undersigned, the undersigned certifies that the information set forth in this
Statement is true, complete and correct.


Date: March 22, 2004                FIRST NEW YORK SECURITIES L.L.C.

                                    BY: /s/ Mario Maugeri
                                       --------------------------------
                                       Name:  Mario Maugeri
                                       Title: Director of Operations


                                    /s/ Jay Goldstein
                                    -----------------------------------
                                    Jay Goldstein


                                    /s/ Douglas Lipton
                                    -----------------------------------
                                    Douglas Lipton


                                    /s/ Michael Marvin
                                    -----------------------------------
                                    Michael Marvin



                                                                       Exhibit 1


                            AGREEMENT OF JOINT FILING


      Pursuant to rule 13d-1(k) promulgated under the Securities Exchange Act of
1934, as amended, the undersigned persons hereby agree to file with the
Securities and Exchange Commission the Statement on Schedule 13G (the
"Statement") to which this Agreement is attached as an exhibit, and agree that
such Statement, as so filed is on the behalf of each of them.

      IN WITNESS WHEREOF, the undersigned have executed this Agreement as of
March 22, 2004.



                                    FIRST NEW YORK SECURITIES L.L.C.

                                    BY: /s/ Mario Maugeri
                                       ----------------------------------
                                       Name:  Mario Maugeri
                                       Title: Director of Operations


                                    /s/ Jay Goldstein
                                    -------------------------------------
                                    Jay Goldstein


                                    /s/ Douglas Lipton
                                    -------------------------------------
                                    Douglas Lipton


                                    /s/ Michael Marvin
                                    -------------------------------------
                                    Michael Marvin