Exhibit 10.4

AMENDMENT NO. 2
TO
EMPLOYMENT AND NON-COMPETITION AGREEMENT
BETWEEN
HORIZON OFFSHORE, INC. AND J. LOUIS FRANK

     This Amendment No. 2 to Employment and Non-Competition Agreement between
Horizon Offshore, Inc. (the “Company”) and J. Louis Frank (the “Employee”) dated
May 31, 2002, as amended on September 3, 2004 (the “Amendment No. 2”), is dated
as of November 4, 2004.

     In mutual consideration of supporting a proposed recapitalization of the
Company, the Company and Employee agree as follows:

     1. The Employment and Non-Competition Agreement between Horizon Offshore,
Inc. and J. Louis Frank dated May 31, 2002, as amended on September 3, 2004,
shall hereinafter be referred to as the “Employment Agreement.”

     2. Section 5(d) of the Employment Agreement shall be amended in its
entirety to read as follows:

“5(d) As used herein, “For Good Cause” shall mean breach of any provision of
this Agreement by the Company and failure to remedy such breach within thirty
(30) days of written notice; failure of the Employee to be elected to the Board
or to be elected by the Board as its Chairman, Emeritus or the relocation of the
Employee’s place of employment outside the Houston Metropolitan area.”

     3. Except as specifically set forth above all other terms, conditions,
rights, obligations and duties of the Employment Agreement shall remain in full
force and effect.

     4. This Amendment No. 2 shall be governed by and interpreted in accordance
with the laws of the State of Texas.

     IN WITNESS WHEREOF, the parties have executed this Amendment No. 2 as of
the date hereinabove.

            HORIZON OFFSHORE, INC.
      By:   /s/ Bill J. Lam        Bill J. Lam        President     

            EMPLOYEE
      /s/ J. Louis Frank        J. Louis Frank