EXHIBIT 4

                                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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