SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   -----------

                                   SCHEDULE TO
                                 (Rule 14d-100)

      TENDER OFFER STATEMENT UNDER SECTION 14(d)(1) OR SECTION 13(e)(1) OF
                       THE SECURITIES EXCHANGE ACT OF 1934

                                 AMENDMENT NO. 4

                             Rare Medium Group, Inc.
                             ----------------------
                       (Name of Subject Company (Issuer))

                             AP/RM Acquisition, LLC
                             ----------------------
                        (Name of Filing Person (Offeror))

                         Apollo Investment Fund IV, L.P.
                            Apollo Advisors IV, L.P.
                         ------------------------------
                (Names of Filing Persons (Affiliates of Offeror))

                     Common Stock, Par Value $0.01 Per Share
                     ---------------------------------------
                           (Title of Class Securities)

                                    75382N109
                       -----------------------------------
                      (CUSIP Number of Class of Securities)

                                Michael D. Weiner
                             AP/RM Acquisition, LLC
                             Two Manhattanville Road
                            Purchase, New York 10577
                                 (914) 694-8000
                      -------------------------------------
                  (Name, Address and Telephone Number of Person
  Authorized to Receive Notices and Communications on Behalf of Filing Persons)

                                 With a copy to:

                              Paul A. Belvin, Esq.
                    Akin, Gump, Strauss, Hauer & Feld, L.L.P.
                         1333 New Hampshire Avenue, N.W.
                             Washington, D.C. 20036
                                 (202) 887-4000

                            CALCULATION OF FILING FEE
   -------------------------------------------------------------------------

           Transaction Valuation*                 Amount of Filing Fee
   -------------------------------------------------------------------------
              $ 4,200,814.50                          $ 386.47
   -------------------------------------------------------------------------

* For purposes of calculating the filing fee only, this amount is based on the
  purchase of 15,002,909 outstanding shares of Common Stock at the tender offer
  price of $0.28 per share.

[X] Check the box if any part of the fee is offset as provided by Rule 0-11 (a)
    (2) and identify the filing with which the offsetting fee was previously
    paid. Identify the previous filing by registration statement number, or the
    Form or Schedule and the date of its filing.


                                                       
Amount Previously Paid:      $386.47                      Filing Party::     AP/RM Acquisition, LLC
                       ---------------------------                      ------------------------------
Form or Registration No.:  Schedule TO                    Date Filed::         April 9, 2002
                         -------------------------                    -----------------------------


 [_] Check the box if the filing relates solely to preliminary communications
     made before the commencement of a tender offer.
     Check the appropriate boxes below to designate any transactions to which
     the statement relates:

     [X] third-party tender offer subject to Rule 14d-1.
     [_] issuer tender offer subject to Rule 13e-4.
     [_] going-private transaction subject to Rule 13e-3.
     [_] amendment to Schedule 13D under Rule 13d-2.
     Check the following box if the filing is a final amendment reporting the
     results of the tender offer: [X]



                  This Amendment No. 4 amends and supplements the Tender Offer
Statement on Schedule TO filed with the Securities and Exchange Commission (the
"Commission") on April 9, 2002, as amended by Amendment No. 1 thereto filed with
the Commission on April 23, 2002, Amendment No. 2 thereto filed with the
Commission on May 1, 2002 and Amendment No. 3 thereto filed with the Commission
on May 8, 2002 (the "Schedule TO"), by AP/RM Acquisition, LLC, a Delaware
limited liability company (the "Purchaser"), in connection with the offer by the
Purchaser to purchase up to 15,002,909 shares of common stock, par value $0.01
per share (the "Common Stock"), of Rare Medium Group, Inc., a Delaware
corporation (the "Company"), at a price of $0.28 per share of Common Stock, net
to the seller in cash, without interest and subject to the terms and conditions
set forth in the Offer to Purchase, dated April 9, 2002 (the "Offer to
Purchase"), and the related Letter of Transmittal (the "Letter of Transmittal"),
which together, as each may be amended or supplemented from time to time,
constitute the "Offer" and which are annexed to and filed with the Schedule TO
as Exhibits (a)(1)(i) and (a)(1)(ii), respectively. Capitalized terms used
herein but not otherwise defined have the meaning ascribed to such terms in the
Offer to Purchase.

Items 1,4 and 8.

                  Items 1, 4 and 8 are hereby amended and supplemented as
follows:

                  The Offer expired at 5:00 p.m., New York City time, on Friday,
May 10, 2002. Pursuant to the Offer, based upon a report from the Depositary, on
May 13, 2002, the Purchaser accepted for payment 4,800,643 shares of Common
Stock (including shares of Common Stock delivered pursuant to guaranteed
delivery).

                  On May 13, 2002, the Purchaser issued a press release
announcing the completion of the Offer. The press release is contained in
Exhibit (a)(5)(vii) hereto, and the information set forth in the press release
is hereby incorporated by reference.

Item 12.          Exhibits

                  Item 12 is hereby amended and supplemented to add thereto the
following:

EXHIBIT NUMBER          DESCRIPTION
--------------          -----------

(a)(5)(vii)             Press release dated May 13, 2002.



                                   SIGNATURES

                  After due inquiry and to the best of my knowledge and belief,
I certify that the information set forth in this statement is true, complete and
correct.


                                    AP/RM ACQUISITION, LLC



Dated: May 13, 2002                 By:      Apollo Management IV, L.P.
                                             its general partner


                                    By:      AIF IV Management, Inc.
                                             its general partner

                                    By:_______________________________
                                         Name:    Andrew D. Africk
                                         Title:   Vice President


                                    APOLLO INVESTMENT FUND IV, L.P.


Dated: May 13, 2002                 By:      Apollo Advisors IV, L.P.
                                             its general partner


                                    By:      Apollo Capital Management IV, Inc.
                                             its general partner

                                    By: ______________________________
                                         Name:    Andrew D. Africk
                                         Title:   Vice President


                                    APOLLO ADVISORS IV, L.P.


Dated: May 13, 2002                 By:      Apollo Capital Management IV, Inc.
                                             its general partner

                                    By:_______________________________
                                         Name:    Andrew D. Africk
                                         Title:   Vice President



                                  EXHIBIT INDEX

Exhibit Number              Description
--------------              -----------

(a)(5)(vii)                 Press release dated May 13, 2002.