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                                                                     EXHIBIT 4.1


                                AMENDMENT NO. 1
                                      TO
                               RIGHTS AGREEMENT


     Amendment No. 1, dated as of September 30, 1997, to the Rights Agreement,
dated as of February 13, 1996 (the "Agreement"), between United Meridian
Corporation, a Delaware corporation (the "Company"), and Chemical Mellon
Shareholder Services, L.L.C., a New Jersey limited liability company (the
"Rights Agent").



                             W I T N E S S E T H:
                             - - - - - - - - - - 


     WHEREAS, the Company and the Rights Agent executed and delivered the
Agreement specifying the terms of the Rights (as defined therein);

     WHEREAS, subsequent to the execution of the Agreement, the Rights Agent
changed its name to ChaseMellon Shareholder Services, L.L.C.; and

     WHEREAS, the Board of Directors of the Company deems it desirable to amend
the Agreement pursuant to the provisions of Section 26 of the Agreement to make
certain modifications to the Agreement upon the terms and conditions hereinafter
set forth, such modifications to be effective on the date hereinafter set forth.

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

     1.  The definition of the term "Acquiring Person" set forth in Section 1(a)
of the Agreement is hereby amended to read in its entirety as follows:


         "`Acquiring Person' shall mean any Person (as such term is hereinafter
     defined) who or which, together with all Affiliates (as such term is
     hereinafter defined) and Associates (as such term is hereinafter defined)
     of such Person, shall be the Beneficial Owner (as such term is hereinafter
     defined) of 10% or more of the Voting Stock (as such term is hereinafter
     defined) of the Company then outstanding; provided, that, an Acquiring
     Person shall not include (i) an Exempt Person (as such term is hereinafter
     defined), or (ii) any Person, together with all Affiliates and Associates
     of such Person, who or which would be an Acquiring Person solely by reason
     of (A) being the Beneficial Owner of shares of Voting Stock of the Company,
     the Beneficial Ownership of which was acquired by such Person pursuant to
     any action or transaction or series of related actions or transactions
     approved by the Board of Directors before such Person otherwise became an
     Acquiring Person, or (B) a reduction in the number of issued and
     outstanding shares of Voting Stock of the Company pursuant to a transaction
     or a series of related transactions approved by the Board of Directors of
     the Company;

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     provided, further, that in the event such Person described in this clause
     (ii) does not become an Acquiring Person by reason of subclause (A) or (B)
     of this clause (ii), such Person nonetheless shall become an Acquiring
     Person in the event such Person thereafter acquires Beneficial Ownership of
     an additional 1% or more of the Voting Stock of the Company, unless the
     acquisition of such additional Voting Stock would not result in such Person
     becoming an Acquiring Person by reason of subclause (A) or (B) of this
     clause (ii). Notwithstanding the foregoing, if the Board of Directors of
     the Company determines in good faith (but only if at the time of such
     determination by the Board of Directors there are then in office not less
     than a majority of directors who are Continuing Directors (as such term is
     hereinafter defined) and such action is approved by a majority of the
     Continuing Directors then in office) that a Person who would otherwise be
     an "Acquiring Person" as defined pursuant to the foregoing provisions of
     this paragraph (a) has become such inadvertently, and such Person divests
     as promptly as practicable a sufficient number of shares of Voting Stock so
     that such Person would no longer be an "Acquiring Person" as defined
     pursuant to the foregoing provisions of this paragraph (a), then such
     Person shall not be deemed an "Acquiring Person" for any purposes of this
     Rights Agreement."


     2.  This Amendment No. 1 to the Agreement shall become effective as of the
close of business on September 30, 1997.  This Amendment No. 1 to the 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.

     3.  Except as specifically provided in this Amendment No. 1 to the
Agreement, the Agreement shall remain in full force and effect and shall in no
way be amended, modified or affected hereby.

     IN WITNESS WHEREOF, the parties hereto have caused this Amendment No. 1 
to the Agreement to be duly executed, all as of the day and year first 
above-written.

                    UNITED MERIDIAN CORPORATION


                    By:     /s/ Jonathan M. Clarkson
                            ------------------------
                    Name:   Jonathan M. Clarkson
                    Title:  Executive Vice President and Chief Financial Officer



                    CHASEMELLON SHAREHOLDER SERVICES, L.L.C.

                    By:     /s/ R. John Davis
                            -----------------
                    Name:   R. John Davis
                    Title:  Vice President

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