<PAGE>

                                                                     EXHIBIT 4.1


                     AMENDMENT NO. 1 TO THE RIGHTS AGREEMENT


     Amendment No. 1 to the Rights Agreement, dated as of June 15, 2002, by and
between Zimmer Holdings, Inc. (the "Company") and Mellon Investor Services LLC
(the "Rights Agent").

     WHEREAS, the Company and the Rights Agent have entered into that certain
Rights Agreement, dated as of July 30, 2001 (the "Rights Agreement"); and

     WHEREAS, on June 15, 2002, the Company, by resolution adopted by its Board
of Directors, determined to amend the Rights Agreement.

     NOW, THEREFORE, in consideration of the premises and the mutual agreements
set forth herein, the parties hereto do hereby agree as follows:

1.   The Rights Agreement is hereby amended as follows:

     (a)  The definition of "Acquiring Person" in Section 1 of the Rights
Agreement is hereby amended and restated in its entirety as follows:

          "'ACQUIRING PERSON' shall mean any Person who or which, alone or
          together with all Affiliates and Associates of such Person, shall be
          the Beneficial Owner of more than 20% of the Common Shares then
          outstanding, but shall not include (a)(i) the Company, any Subsidiary
          of the Company, any employee benefit or compensation plan of the
          Company or of any of its Subsidiaries or any Person holding Common
          Shares for or pursuant to the terms of any such employee benefit or
          compensation plan or for the purpose of funding other employee
          benefits for employees of the Company or of any Subsidiary of the
          Company and (ii) until immediately after the distribution of the
          Common Shares of the Company by the sole stockholder of the Company,
          Bristol-Myers Squibb Company ("BRISTOL-MYERS SQUIBB"), to the
          stockholders of Bristol-Myers Squibb, Bristol-Myers Squibb or any
          Affiliate or Associate thereof (each Person covered by clauses (a)(i)
          and (a)(ii), an "EXEMPT PERSON"), or (b) any such Person that the
          Board of Directors of the Company determines has become the Beneficial
          Owner of more than 20% of the Common Shares at the time outstanding
          solely as the result of (i) a change in the aggregate number of Common
          Shares outstanding since the last date on which such Person acquired
          Beneficial Ownership of any Common Shares (PROVIDED, HOWEVER, that if
          a Person becomes the Beneficial Owner of more than 20% of the Common
          Shares then outstanding by reason of such change in the aggregate
          number of Common Shares outstanding and thereafter becomes the
          Beneficial Owner of any additional Common Shares (other than pursuant
          to a dividend or distribution paid or made

                                       1
<PAGE>

          by the Company on the outstanding Common Shares or pursuant to a split
          or subdivision of the outstanding Common Shares), then such Person
          shall be deemed to be an "Acquiring Person" unless upon becoming the
          Beneficial Owner of such additional Common Shares such Person does not
          beneficially own more than 20% of the shares of Common Shares then
          outstanding), (ii) the acquisition by such Person or one or more of
          its Affiliates or Associates of Beneficial Ownership of additional
          Common Shares if such acquisition was made in the good faith belief
          that such acquisition would not (A) cause the Beneficial Ownership by
          such Person, together with its Affiliates and Associates, to exceed
          20% of the Common Shares outstanding at the time of such acquisition
          and such good faith belief was based on the good faith reliance on
          information contained in publicly filed reports or documents of the
          Company that are inaccurate or out-of-date or (B) otherwise cause a
          Distribution Date or the adjustment provided for in Section 11(a) to
          occur, or (iii) the acquisition by such Person or one or more of its
          Affiliates or Associates of Beneficial Ownership of additional Common
          Shares if the Board of Directors of the Company determines that such
          acquisition was made in good faith without the knowledge by such
          Person or one or more of its Affiliates or Associates that such Person
          would thereby become an Acquiring Person and without the intention of
          changing or influencing control of the Company (including, without
          limitation, because (A) such Person was unaware that it beneficially
          owned a percentage of Common Shares that would otherwise cause such
          Person to be an Acquiring Person or (B) such Person was aware of the
          extent of its Beneficial Ownership of Common Shares but had no actual
          knowledge of the consequences of such Beneficial Ownership under this
          Rights Agreement), which determination of the Board of Directors of
          the Company shall be conclusive and binding on such Person, the Rights
          Agent, the holders of the Rights and all other Persons.
          Notwithstanding clause (b)(ii) or (b)(iii) of the prior sentence, if
          any Person that is not an Acquiring Person due to such clause (b)(ii)
          or (b)(iii) does not reduce its percentage of Beneficial Ownership of
          Common Shares to 20% or less by the Close of Business on the tenth
          calendar day, or such other calendar day as determined, in good faith,
          by the Board of Directors of the Company, after notice from the
          Company (the date of notice being the first day) that such Person's
          Beneficial Ownership of Common Shares would make it an Acquiring
          Person, such Person shall, at the end of the later of (x) such ten
          calendar day period and (y) such other calendar day as determined by
          the Board of Directors of the Company, become an Acquiring Person (and
          such clause (b)(ii) or (b)(iii) shall no longer apply to such Person).
          For purposes of this definition, the determination whether any Person
          acted in "good faith" shall be conclusively determined by the Board of
          Directors of the Company."

     (b)  All references to "15%" in Section 3(b) or any other section of the
Rights Agreement relating to the Beneficial Ownership of the Common Shares shall
be deemed to be references to "20%."

2.   The Rights Agreement shall not otherwise be supplemented or amended by
virtue of this Amendment No. 1 to the Rights Agreement, but shall remain in full
force and effect.

                                       2
<PAGE>

3.   Capitalized terms used without other definition in this Amendment No. 1 to
the Rights Agreement shall be used as defined in the Rights Agreement.

4.   This Amendment No. 1 to the Rights Agreement shall be deemed to be a
contract made under the laws of the State of Delaware and for all purposes shall
be governed by and construed in accordance with the laws of such State
applicable to contracts to be made and performed entirely within such State;
provided, however, that all provisions regarding the rights, duties and
obligations of the Rights Agent shall be governed by and construed in accordance
with the laws of the State of New York applicable to contracts made and to be
performed entirely within such State.

5.   This Amendment No. 1 to the Rights Agreement may be executed in any number
of counterparts and each of such counterparts shall for all purposes be deemed
to be an original, and all such counterparts shall together constitute but one
and the same instrument.

6.   All references to the Rights Agreement shall, from and after the execution
of this Amendment No. 1 to the Rights Agreement, be deemed to be references to
the Rights Agreement as amended hereby.

7.   Exhibits B and C to the Rights Agreement shall be deemed amended in a
manner consistent with this Amendment No. 1 to the Rights Agreement.

     IN WITNESS WHEREOF, the parties have executed this Amendment No. 1 to the
Rights Agreement as of the date written above.


                                      ZIMMER HOLDINGS, INC.


                                      By:
                                          -------------------------------



                                      MELLON INVESTOR SERVICES LLC


                                      By:
                                          -------------------------------



                                       3