AMENDMENT TO RIGHTS AGREEMENT

EXHIBIT 4.13

AMENDMENT TO

RIGHTS AGREEMENT

This Amendment to Rights Agreement dated as of March 5, 2004 (“Amendment”) amends that certain Rights Agreement (“Agreement”) dated as of June 18, 2003 by and between Hornbeck Offshore Services, Inc., a Delaware corporation (“Company”), and Mellon Investor Services LLC, a New Jersey limited liability company (“Rights Agent”).

WHEREAS, the Company intends to make a public offering of its common stock and in connection therewith to effect a reverse stock split of its common stock;

WHEREAS, the Board of Directors of the Company has determined that in connection with such public offering and reverse stock split it would be in the best interests of the Company to amend the Agreement to establish a greater majority of the Board for certain actions taken in accordance with the Agreement and to maintain for each holder of the Company’s common stock, following the public offering and the reverse stock split, one Right (as such term is defined in the Agreement) for each share of the Company’s common stock then outstanding and held by each such holder;

WHEREAS, the Agreement permits the Company to amend the Agreement, without action of the holders of the Rights, if the Rights are then redeemable, and the Rights are currently redeemable;

WHEREAS, the Rights Agent has agreed under the Agreement to execute any such amendment if, among other things, such amendment does not affect the rights, duties, obligations or immunities of the Rights Agent under the Agreement; and

WHEREAS, the Board of Directors of the Company has determined that this Amendment does not affect the rights, duties, obligations or immunities of the Rights Agent under the Agreement;

NOW THEREFORE, in consideration of the premises set forth above, the parties hereby agree as follows:

1. Clause (ii)(B) of the definition of “Acquiring Person” in Section 1 of the Agreement is hereby amended to add the language indicated in italics below:

“being the Beneficial Owner of shares of Common Stock, 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 at least 80% of the members of the full Board of Directors before such Person otherwise becomes an Acquiring Person; or”

2. Section 7(b) of the Agreement is hereby amended to read as follows:

“The Purchase Price for each one one-hundredth of a share of Preferred Stock issued pursuant to the exercise of a Right shall initially be $187.50, shall be subject to adjustment from time to time as provided in Sections 11 and 13 hereof and shall be payable in lawful money of the United States of America, in accordance with paragraph 7(c) below.”

3. The third sentence of Section 11(d) of the Agreement is hereby amended to add the language indicated in italics below:

“For the purpose of any computation hereunder, if the Preferred Stock is not publicly traded but the shares of Common Stock are publicly traded, the “Current Market Price” per share of the Preferred Stock shall be conclusively deemed to be the Current Market Price per share of Common Stock multiplied by 100 (appropriately adjusted to reflect any stock split, stock dividend or similar transaction occurring after the date hereof, other than the reverse stock split contemplated in the Amendment to Rights Agreement dated as of March 5, 2004 between the Company and the Rights Agent (the “Amendment”)).”

4. The first sentence of Section 24(a) of the Agreement is hereby amended to add the language indicated in italics below:

“The Company may, at its option, but only by the vote of a majority of the Board of Directors, at any time and from time to time after the first occurrence of a Flip-In Event, exchange all or part of the then outstanding and exercisable Rights (which shall not include Rights that have become null and void pursuant to the provisions of Section 7(e) hereof) for shares of its Common Stock at an exchange ration of one share of its Common Stock per Right, appropriately adjusted to reflect any stock split, stock dividend or similar transaction occurring after the date hereof, other than the reverse stock split contemplated in the Amendment (such exchange ratio being hereinafter referred to as the “Exchange Ratio”).

5. In accordance with Section 31 of the Agreement and notwithstanding anything to the contrary elsewhere in the Agreement, at the effective time of the reverse stock split, each Right associated with each share of Common Stock shall undergo the same reverse split, such that, immediately following the effective time of the reverse stock split, one Right shall continue to be associated with each share of Common Stock outstanding immediately after the effective time of the reverse stock split, and one Right shall be issued with respect to each share of Common Stock that shall become outstanding between the date such reverse stock split is accomplished and the earliest of the Distribution Date and the Expiration Date.

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6. Except as expressly modified by this Amendment, all of the terms, covenants, agreements, conditions and other provisions of the Rights Agreement shall remain in full force and effect in accordance with their respective terms. As used in the Agreement, the terms “this Agreement,” “herein,” “hereinafter,” “hereunder,” “hereto” and words of similar import shall mean and refer to, from and after the date of this Amendment, unless the context otherwise requires, the Agreement as amended by this Amendment.

7. Capitalized terms used in this Amendment and not otherwise defined herein shall have the meanings given to such terms in the Agreement.

8. This Amendment may be executed in one or more counterparts, and signature pages may be delivered by facsimile, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument, and shall become effective upon its execution by the parties hereto.

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IN WITNESS WHEREOF, the parties have executed and delivered this Amendment to the Agreement effective as of the date first above written.

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