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                                                                     EXHIBIT 4.3

                       FIRST AMENDMENT TO RIGHTS AGREEMENT

         FIRST AMENDMENT, dated as of February 26, 2004 (this "Amendment"), to
the Rights Agreement, dated effective as of April 10, 2001 (the "Rights
Agreement"), between ILEX Oncology, Inc., a Delaware corporation (the
"Company"), and American Stock Transfer & Trust Company, as Rights Agent (the
"Rights Agent").

                              W I T N E S S E T H:

         WHEREAS, the Company is entering into an Agreement and Plan of Merger
dated February 26, 2004 (as the same may be amended from time to time, the
"Merger Agreement"), among the Company, Genzyme Corporation, a Massachusetts
corporation ("Parent"), GLBC Corp., a Delaware corporation ("Sub"), and GLBC
LLC, a Delaware limited liability company ("LLC"), pursuant to which, among
other things, Sub shall be merged with and into the Company and the Company will
become a wholly-owned subsidiary of Parent, the Company shall be merged with and
into LLC and the outstanding capital stock of the Company will be converted into
the right to receive shares of Parent common stock, $0.01 par value per share;

         WHEREAS, the Company and the Rights Agent have heretofore executed and
entered into the Rights Agreement;

         WHEREAS, pursuant to Section 27 of the Rights Agreement, prior to a
Distribution Date (as defined therein), the Company and the Rights Agent may
from time to time supplement or amend the Rights Agreement in any respect
without approval of any holders of the Rights Certificates (as defined in the
Rights Agreement), whether or not such supplement or amendment is adverse to any
holders of rights under the Rights Agreement; and

         WHEREAS, the parties desire to amend the Rights Agreement in connection
with the execution and delivery of the Merger Agreement, dated as of February
26, 2004, among Parent, Sub, LLC and the Company; and

         WHEREAS, the Board of Directors of the Company has determined that this
Amendment is in the best interests of holders of the Rights Certificates;

         NOW, THEREFORE, in consideration of the foregoing and the mutual
agreements set forth herein, the Company and the Rights Agent agree as follows:

         1.       Section 1(a) of the Rights Agreement is hereby amended and
restated to read in its entirety as follows:

         "Acquiring Person" shall mean any Person who or which, together with
         all Affiliates and Associates of such Person, shall be the Beneficial
         Owner of 20% or more of the Common Shares then outstanding, but shall
         not include (i) the Company; (ii) any Subsidiary of the Company; (iii)
         any employee benefit plan of the Company or of any Subsidiary of the
         Company; (iv) any Person holding Common Shares for or pursuant to the
         terms of any such plan to the extent, and only to the extent, of the
         Common Shares so held; and (v) Genzyme Corporation.

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         Notwithstanding the foregoing, no Person shall become an "Acquiring
         Person" as the result of an acquisition of Common Shares by the Company
         which, by reducing the number of shares outstanding, increases the
         proportionate number of shares beneficially owned by such Person to 20%
         or more of the Common Shares then outstanding; provided, however, that
         if a Person becomes the Beneficial Owner of 20% or more of the Common
         Shares then outstanding by reason of share acquisitions by the Company
         and shall, after such share acquisitions by the Company, become the
         Beneficial Owner of any additional Common Shares, then such Person
         shall be deemed to be an "Acquiring Person."

         2.       Section 1(c) of the Rights Agreement is hereby amended and
restated to read in its entirety as follows:

         A Person shall be deemed the "Beneficial Owner" of and shall be deemed
         to "beneficially own" any securities:

                           (i)      which such Person or any of such Person's
         Affiliates or Associates beneficially owns, directly or indirectly;

                           (ii)     which such Person or any of such Person's
         Affiliates or Associates has (A) the right to acquire (whether such
         right is exercisable immediately or only after the passage of time)
         pursuant to any agreement, arrangement or understanding (other than
         customary agreements with and between underwriters and selling group
         members with respect to a bona fide public offering of securities), or
         pursuant to the exercise of conversion rights, exchange rights, rights
         (other than the Rights), warrants or options, or otherwise; provided,
         however, that a Person shall not be deemed the Beneficial Owner of, or
         to beneficially own, securities tendered pursuant to a tender or
         exchange offer made by or on behalf of such Person or any of such
         Person's Affiliates or Associates until such tendered securities are
         accepted for purchase or exchange; or (B) the right to vote or consent
         to action pursuant to any agreement, arrangement or understanding;
         provided, however, that a Person shall not be deemed the Beneficial
         Owner of, or to beneficially own, any security if the agreement,
         arrangement or understanding to vote such security or consent to action
         (1) arises solely from a revocable proxy or consent given to such
         Person in response to a public proxy or consent solicitation made
         pursuant to, and in accordance with, the applicable rules and
         regulations promulgated under the Exchange Act and (2) is not also then
         reportable on Schedule 13D promulgated under the Exchange Act (or any
         comparable or successor report); or

                           (iii)    which are beneficially owned, directly or
         indirectly, by any other Person with which such Person or any of such
         Person's Affiliates or Associates has any agreement, arrangement or
         understanding (other than customary agreements with and between
         underwriters and selling group members with respect to a bona fide
         public offering of securities) for the purpose of acquiring, holding,
         voting or consenting to action (except to the extent

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         contemplated by the proviso to Section 1(c)(iii) hereof) or disposing
         of any securities of the Company.

         Notwithstanding the foregoing, any securities that are owned or held by
         (i) the Company; (ii) any Subsidiary of the Company; (iii) any employee
         benefit plan of the Company or of any Subsidiary of the Company; (iv)
         any securities that are owned or held by any Person pursuant to the
         terms of any such plan (to the extent, and only to the extent, of the
         securities so held); or (v) Genzyme Corporation shall not be deemed to
         be beneficially owned by any other Person and no other Person shall be
         deemed to be the Beneficial Owner of such securities. Further,
         notwithstanding anything in this definition of Beneficial Ownership to
         the contrary, the phrase "then outstanding", when used with reference
         to a Persons Beneficial Ownership of securities of the Company, shall
         mean the number of such securities then issued and outstanding together
         with the number of such securities not then actually issued and
         outstanding which such Person would be deemed to own beneficially
         hereunder.

         3.       Section 3(a) of the Rights Agreement is hereby amended and
restated to read in its entirety as follows:

         Until the earlier (the earlier of such dates being herein referred to
         as the "Distribution Date") of (i) the Close of Business on the tenth
         Business Day after the Shares Acquisition Date and (ii) the Close of
         Business on the tenth Business Day after the date of the commencement
         by any Person (other than the Company, any Subsidiary of the Company,
         any employee benefit plan of the Company or of any Subsidiary of the
         Company, any Person holding Common Shares for or pursuant to the terms
         of any such plan to the extent such Person is so acting with the
         approval or consent of the Company, or Genzyme Corporation) of, or of
         the first public announcement of the intention of any Person (other
         than the Company, any Subsidiary of the Company, any employee benefit
         plan of the Company or of any Subsidiary of the Company, any Person
         holding Common Shares for or pursuant to the terms of any such plan to
         the extent such Person is so acting with the approval or consent of the
         Company, or Genzyme Corporation) to commence, a tender or exchange
         offer the consummation of which would result in any Person becoming the
         Beneficial Owner of 20% or more of the Common Shares then outstanding,
         including any such date which is after the date of this Agreement and
         prior to the issuance of the Rights, (x) the Rights will be evidenced
         (subject to the provisions of Section 3(b) hereof) by the certificates
         for Common Shares registered in the names of the holders thereof (which
         certificates shall also be deemed to be Right Certificates) and not by
         separate Right Certificates, and (y) the right to receive Right
         Certificates will be transferable only in connection with the transfer
         of Common Shares of the Company. As soon as practicable after the
         Distribution Date, the Company will prepare and execute, the Rights
         Agent will countersign, and the Company will send or cause to be sent
         (and the Rights Agent will, if requested and provided with all
         necessary information, send), by first-class, insured, postage prepaid
         mail, to each record holder of Common Shares as

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         of the Close of Business on the Distribution Date, at the address of
         such holder shown on the records of the Company, a Right Certificate,
         in substantially the form of Exhibit B hereto (a "Right Certificate"),
         evidencing one Right for each Common Share of the Company so held. As
         of the Distribution Date, the Rights will be evidenced solely by such
         Right Certificates.

         4.       Section 13(c) is hereby incorporated into the Rights Agreement
and will read as follows:

         (c) Notwithstanding the provisions of this Section 13, upon the
         occurrence of the Mergers (as defined in the Agreement and Plan of
         Merger, dated February 26, 2004, by and among Genzyme Corporation, GLBC
         Corp., GLBC LLC and the Company, as may be amended from time to time
         (the "Merger Agreement")), this Agreement shall terminate and the
         Rights will be cancelled and extinguished in accordance with the
         provisions of the Merger Agreement.

         5.       Section 25(a) of the Rights Agreement is hereby amended and
restated to read in its entirety as follows:

         In case the Company shall propose (i) to pay any dividend payable in
         stock of any class to the holders of Preferred Shares or to make any
         other distribution to the holders of Preferred Shares (other than a
         regular quarterly cash dividend), (ii) to offer to the holders of
         Preferred Shares rights (preemptive or otherwise) or warrants to
         subscribe for or to purchase any additional Preferred Shares or shares
         of stock of any class or any other securities, rights or options, (iii)
         to effect any reclassification of Preferred Shares (other than a
         reclassification involving only the subdivision of outstanding
         Preferred Shares), (iv) except with respect to the Mergers (as defined
         in the Merger Agreement), to effect any consolidation or merger into or
         with, or to effect any sale or other transfer (or to permit one or more
         of its Subsidiaries to effect any sale or other transfer), in one or
         more transactions, of 50% or more of the assets or earning power of the
         Company and its Subsidiaries (taken as a whole) to, any other Person,
         (v) to effect the liquidation, dissolution or winding up of the
         Company, or (vi) to declare or pay any dividend on the Common Shares
         payable in Common Shares, to reclassify the Common Shares, or to
         otherwise effect a split-up, division or combination of the Common
         Shares, then, in each such case, the Company shall give to each holder
         of a Right Certificate and the Rights Agent, in accordance with Section
         26 hereof, a notice of such proposed action, which shall specify the
         record date for purposes of such stock dividend, or distribution of
         rights or warrants, or the date on which such reclassification,
         consolidation, merger, sale, transfer, liquidation, dissolution, or
         winding up is to take place and the date of participation therein by
         the holders of the Common Shares and/or Preferred Shares, if any such
         date is to be fixed, and such notice shall be so given in the case of
         any action described by clause (i) or (ii) above at least ten days
         prior to the record date for determining holders of the Preferred
         Shares for purposes of such action, and in the case of any such other
         action, at least ten days prior to the date of the taking of such
         proposed action or

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         the date of participation therein by the holders of the Common Shares
         and/or Preferred Shares, whichever shall be the earlier.

         6.       This Amendment shall be governed by and construed in
accordance with the laws of the State of Delaware.

         7.       This Amendment may not be amended or modified, and no
provision hereof may be waived, except in accordance with Section 27 of the
Rights Agreement.

         8.       Except as otherwise modified by this Amendment, the provisions
of the Rights Agreement shall continue to be and remain in full force and
effect.

         9.       This Amendment may be executed in two or more counterparts,
each of which shall be deemed an original, but all of which together shall
constitute one and the same instrument.

                         [signatures on following page]

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         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed as of the day and year first above written.

                                         ILEX ONCOLOGY, INC.

                                         By:     /s/ Jeffrey H. Buchalter
                                            ------------------------------------
                                                 Jeffrey H. Buchalter
                                                 President and CEO

                                         AMERICAN STOCK TRANSFER AND TRUST
                                         CO., as Rights Agent

                                         By:     /s/ Herbert J. Lemmer
                                            ------------------------------------
                                                 Herbert J. Lemmer
                                                 Vice President

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