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                                                                     EXHIBIT 10g


                              ROWAN COMPANIES, INC


AMENDMENT NO. 4 TO THE 1986 CONVERTIBLE DEBENTURE INCENTIVE PLAN:


         WHEREAS, there is reserved to the Committee in Section 10 of the Rowan
         Companies, Inc. 1986 Convertible Debenture Incentive Plan (the "Plan")
         the right to amend the Plan in whole or in part at any time and in
         such manner as it may deem advisable, subject to certain restrictions
         set forth in the Plan; be it

         RESOLVED, THAT, Section 3.03 of the Plan is hereby amended effective
         as of July 24, 1996, by adding thereto the following:

                 Notwithstanding the foregoing or any provision in the Plan to
the contrary, effective with the occurrence of a Corporate Change, as defined
in the Company's 1988 Nonqualified Stock Option Plan, each Debenture that has
been issued and outstanding for more than one year as of the date of the
Corporate Change shall automatically be fully convertible on and after the date
of such Corporate Change.