FORM 4


                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549


                 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP


[ ] Check this box if no longer subject
    to Section 16. Form 4 or Form 5
    obligations may continue.  See
    Instruction 1(b).


    Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934,
       Section 17(a) of the Public Utility Holding Company Act of 1935 or
              Section 30(f) of the Investment Company Act of 1940

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1. Name and Address of Reporting Person*

   HX Investors, L.P.(1)
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   (Last)            (First)            (Middle)

   100 Jericho Quadrangle, Suite 214
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                     (Street)

   Jericho              New York        11753
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   (City)               (State)         (Zip)

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2. Issuer Name and Ticker or Trading Symbol

   Shelbourne Properties I, Inc. (HXD)

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3. IRS or Social Security Number of Reporting Person (Voluntary)



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4. Statement for Month/Year

   6/01

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5. If Amendment, Date of Original (Month/Year)



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6. Relationship of Reporting Person to Issuer
   (Check all applicable)

   [ ] Director                             [X] 10% Owner
   [ ] Officer (give title below)           [ ] Other (specify below)


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7. Individual or Joint/Group Filing (Check applicable line)

   [ ] Form filed by one Reporting Person
   [X] Form filed by more than One Reporting Person

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                        TABLE I -- Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
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                                                                                    5. Amount of     6. Owner-
                                                                                       Securities       ship
                        2. Trans-     3. Trans-       4. Securities Acquired (A)       Beneficially     Form:
                           action        action          or Disposed of (D)            Owned at         Direct      7. Nature of
                           Date          Code            (Instr. 3, 4 and 5)           End of           (D) or         Indirect
1. Title of Security       (Month/    (Instr. 8)      --------------------------       Month            Indirect       Beneficial
   (Instr. 3)              Day/       ----------      Amount    (A) or     Price       (Instr.          (I)            Ownership
                           Year)      Code    V                 (D)                    3 and 4)         (Instr. 4)     (Instr. 4)
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Common Stock            6/18/02        P               300       A         $43.25                       (1)(2)          (1)(2)
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Common Stock            6/19/02        P              4,200      A         $43.21                       (1)(2)          (1)(2)
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Common Stock            6/20/02        P              4,500      A         $43.09                       (1)(2)          (1)(2)
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Common Stock            6/21/02        P               172       A         $43.10                       (1)(2)          (1)(2)
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Common Stock            6/24/02        P               500       A         $43.10                       (1)(2)          (1)(2)
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Common Stock            6/25/02        P               700       A         $43.00                       (1)(2)          (1)(2)
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Common Stock            6/26/02        P               200       A         $43.10                       (1)(2)          (1)(2)
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Common Stock            6/27/02        P               400       A         $43.10                       (1)(2)          (1)(2)
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Common Stock            6/28/02        P              3,000      A         $43.48       100,700         (1)(2)          (1)(2)
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* If the form is filed by more than one Reporting Person, see Instruction 4(b)(v).
Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.






FORM 4 (continued)



                           TABLE II -- Derivative Securities Acquired, Disposed of, or Beneficially Owned
                                    (e.g. puts, calls, warrants, options, convertible securities)
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    1.        2.        3.         4.         5.             6.                 7.           8.        9.         10.       11.
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                                                                           Title and                           Ownership
                                          Number of     Date Exer-         Amount of                           Form of
                                          Derivative    cisable and        Underlying              Number of   Deriv-
                                          Securities    Expiration         Securities      Price   Derivative  ative
            Conver-             Trans-    Acquired (A)  Date (Month/       (Instr. 3       of      Securities  Security:
            sion or   Trans-    action    or Disposed    Day/Year)          and 4)         Deriv-  Benefi-     Direct
            Exercise  action    Code      of (D)        --------------    --------------   ative   cially      (D) or    Nature of
Title of    Price of  Date      (Instr.   (Instr. 3,    Date                      Amount   Secur-  Owned at    Indirect  Indirect
Derivative  Deriv-    (Month/    8)        4 and 5)     Exer-    Expir-           or Num-  ity     End of      (I)       Beneficial
Security    ative      Day/     --------  ----------    cis-     ation            ber of   (Instr. Month       (Instr.   Ownership
(Instr. 3)  Security   Year)    Code  V   (A)   (D)     able     Date     Title   Shares    5)     (Instr. 4)   4)       (Instr. 4)
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Explanation of Responses:

(1)  This statement is filed as a joint report pursuant to Rule 16a-3(j)
     promulgated under the Securities Exchange Act of 1934 (the "Act") by the
     undersigned Reporting Person and by the entities listed on the attached
     Joint Filer Information Sheet who are deemed to constitute a "group"
     beneficially owning more than 10% of the Issuer' shares of common stock,
     par value $0.01 per share (the "Common Stock") under Section 13(d) of the
     Act. Exeter Capital Corporation ("Exeter") is the sole general partner of
     HX Investors, L.P. ("HX") and Michael L. Ashner is the sole shareholder and
     director of Exeter. Accordingly, for purposes of Section 16 of the Act,
     Exeter and Mr. Ashner may be deemed to beneficially own any securities held
     by reported herein which are held by HX. Further, Exeter holds a .01%
     interest in HX and Mr. Ashner holds a 39.99% interest in HX and,
     accordingly, for purposes of Section 16 of the Act, Exeter and Mr. Ashner
     may be deemed to own an approximately .01% and 40%, respectively,
     beneficial interest in any securities reported herein which are held by HX.

(2)  All shares are held by HX. Exeter and Mr. Ashner do not hold any shares of
     Common Stock. Accordingly, in accordance with the ownership percentages set
     forth in footnote (1) above, for purposes of Section 16 of the Act: (i) HX
     beneficially owns the number of shares of Common Stock listed as held by
     it, (ii) Exeter beneficially owns 10.07 shares of Common Stock, and (iii)
     Mr. Ashner beneficially owns 40,280 shares of Common Stock.


              HX INVESTORS, L.P.
              By:  Exeter Capital Corporation, General Partner




              By: Michael L. Ashner                              7/1/02
              ----------------------------------------     --------------------
              Michael L. Ashner                                   Date


** Intentional misstatements or omissions of facts constitute Federal Criminal
   Violations.  See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).

Note: File three copies of this Form, one of which must be manually signed.
      If space provided is insufficient, see Instruction 6 for procedure.




FORM 4 (continued)

                             Joint Filer Information

Each of the undersigned is jointly filing the attached Initial Statement of
Beneficial Ownership of Securities on Form 3 with respect to the beneficial
ownership of shares of Shelbourne Properties I, Inc. The Designated Filer is HX
Investors, L.P.




                                                        
Name:       Exeter Capital Corporation               Name:       Michael L. Ashner
Address:    100 Jericho Quadrangle                   Address:    c/o Exeter Capital Corporation
            Suite 214                                            100 Jericho Quadrangle
            Jericho, New York  11753                             Suite 214
                                                                 Jericho, New York 11753
Signature:  By:  /s/ Michael L. Ashner               Signature:           /s/ Michael L. Ashner
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                   Michael L. Ashner                                      Michael L. Ashner
                   President