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                                                                   Exhibit 10.41

                                                                  EXECUTION COPY

                               AMENDMENT NO. 1 TO

                          REGISTRATION RIGHTS AGREEMENT

     THIS AMENDMENT NO. 1 (this "Amendment") DATED AS OF MARCH 11, 2004 TO THE
REGISTRATION RIGHTS AGREEMENT (the "Agreement") dated as of December 4, 1997,
among HIGHWOOD PARTNERS, L.P., WESTGATE INTERNATIONAL, L.P. and HORIZON
OFFSHORE, INC. (the "Company").

     The parties hereto agree as follows:

     Section 1. Representation and Warranty of Holders. The parties hereto
(other than the Company) represent and warrant that they are currently the only
Holders (as defined in the Agreement).

     Section 2. New Section 2(a)(iii) of the Agreement. A new Section 2(a)(iii)
of the Agreement is added as follows:

          (iii) Whenever a registration is requested by one or more Holders
     pursuant to this Section 2(a), the Company may include Registrable
     Securities (as defined in the Registration Rights Agreement among the
     Company and the purchasers listed on the signature pages thereof dated as
     of March 11, 2004) in such registration.

     Section 3. Amendment to Section 2(c) of the Agreement. Section 2(c) of the
Agreement is amended to add "2(a) or" immediately prior to "2(b)" in the first
sentence thereof.

     Section 4. Registration. The parties hereto agree that the Company shall be
deemed to have been given on the date hereof a request for a Piggyback
Registration (as defined in the Agreement) pursuant to Section 2(b) of the
Agreement with respect to all Registrable Securities (as defined in the
Agreement).

     Section 5. Counterparts. This Amendment may be executed in one or more
counterparts, each of which shall be deemed an original but all of which taken
together shall constitute a single agreement.

     Section 6. Effectiveness. This Amendment shall become effective upon
signing of all the parties hereto.
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     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed and delivered by their respective officers hereunto duly authorized as
of the date first above written.

                                        HORIZON OFFSHORE, INC.

                                        By:
                                           ------------------------------------
                                           Name:
                                           Title:

                                        ELLIOTT ASSOCIATES, L.P.

                                        By: Elliott Capital Advisors, L.P.,
                                            as General Partner

                                        By: Braxton Associates, Inc.,
                                            as General Partner

                                        By:
                                           ------------------------------------
                                           Name:
                                           Title:

                                        Address: 712 Fifth Avenue
                                                 36th Floor
                                                 New York, New York  10019

                                        ELLIOTT INTERNATIONAL, L.P.

                                        By: Elliott International Capital
                                            Advisors Inc., as Attorney-in-Fact

                                        By:
                                           ------------------------------------
                                           Name:
                                           Title:

                                        Address: 712 Fifth Avenue
                                                 36th Floor
                                                 New York, New York  10019


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