August 8, 2013 Retention Restricted Stock Unit Grant Agreement 2009 McDermott International, Inc. Long-Term Incentive Plan

EXHIBIT 10.4

August 8, 2013 Retention Restricted Stock Unit Grant Agreement

2009 McDermott International, Inc. Long-Term Incentive Plan

On August 8, 2013, the Compensation Committee of the Board of Directors (the “Committee”) of McDermott International, Inc. (“McDermott” or the “Company”) selected you to receive a grant of Restricted Stock Units (“RSUs”) under the 2009 McDermott International, Inc. Long-Term Incentive Plan (the “Plan”) on August 8, 2013 (the “Date of Grant”). The provisions of the Plan are incorporated herein by reference.

Any reference or definition contained in this RSU Grant Agreement (this “Agreement”) shall, except as otherwise specified, be construed in accordance with the terms and conditions of the Plan and all determinations and interpretations made by the Committee with regard to any question arising hereunder or under the Plan shall be binding and conclusive on you and your beneficiaries, estate or personal representatives. The term “Company,” as used in this Agreement with reference to employment or service, shall include subsidiaries of McDermott. Whenever the words “you” or “your” are used in any provision of this Agreement under circumstances where the provision should logically be construed to apply to any beneficiary, estate, or personal representative to whom any rights under this Agreement may be transferred by will or by the laws of descent and distribution, they shall be deemed to include any such person or estate. This Agreement shall be subject to the Company’s Clawback Policy, which is attached hereto as Exhibit A and is incorporated herein by reference.

Restricted Stock Units

RSU Award. You have been awarded the number of RSUs shown on the Notice of Grant dated August 8, 2013, which is incorporated herein by reference. Each RSU represents a right to receive a share of Company common stock on the Vesting Date (as set forth in the “Vesting Requirements” paragraph below), provided the vesting requirements set forth in this Agreement have been satisfied. No shares of common stock are awarded or issued to you on the Date of Grant.

Vesting Requirements. Subject to the “Forfeiture of RSUs” paragraph below, RSUs do not provide you with any rights or interest therein until they become vested under one or more of the following circumstances (each such date a “Vesting Date”):

For purposes of this Agreement, a “Reduction in Force” shall mean a termination of employment with the Company due to elimination of a previously required position or previously required services, or due to the consolidation of departments, abandonment of facilities or offices, technological change or declining business activities, where such termination is intended to be permanent; or under other circumstances which the Compensation Committee, in accordance with standards uniformly applied with respect to all similarly situated employees, designates as a reduction in force.

Forfeiture of RSUs. RSUs which are not and do not become vested upon your termination of employment with the Company for any reason shall, coincident therewith, terminate and be of no further force or effect.

In the event that, while you are employed by the Company or are performing services for or on behalf of the Company under any consulting agreement, (a) you are convicted of (i) a felony or (ii) a misdemeanor involving fraud, dishonesty or moral turpitude, or (b) you engage in conduct that adversely affects or may reasonably be expected to adversely affect the business reputation or economic interests of the Company, as determined in the sole judgment of the Committee, then all RSUs and all rights or benefits awarded to you under this Agreement shall be forfeited, terminated and withdrawn immediately upon (1) notice to the Committee of such conviction pursuant to (a) above or (2) final determination pursuant to (b) above by the Committee. The Committee shall have the right to suspend any and all rights or benefits awarded to you hereunder pending its investigation and final determination with regard to such matters.

Payment of RSUs. RSUs shall be paid in shares of Company common stock, which shares shall be distributed as soon as administratively practicable, but in no event later than 30 days, after the applicable Vesting Date.

Taxes

You will realize income in connection with this grant of RSUs in accordance with the tax laws of the jurisdictions applicable to you.

By acceptance of this Agreement, you agree that any amount which the Company is required to withhold on your behalf, including state income tax and FICA withholding, in connection with income realized by you under this Agreement will be satisfied by withholding whole units or shares having an aggregate fair market value as equal in value but not exceeding the amount of such required tax withholding, unless the Committee determines to satisfy the statutory minimum withholding obligation by another method permitted by the Plan.

Regardless of the withholding method referred to above, you are liable to the Company for the amount of income tax which the Company is required to withhold in connection with the income realized by you in connection with this Agreement, and you hereby authorize the Company to withhold such amount, in whole or in part, from subsequent salary payments, without further notice to you, if the withholding method referred to above is not utilized or does not completely cover such required tax withholding.

Transferability

RSUs granted hereunder are non-transferable other than by will or by the laws of descent and distribution or pursuant to a qualified domestic relations order.

Securities and Exchange Commission Requirements

If you are a Section 16 insider, this type of transaction must be reported on a Form 4 before the end of the second (2^nd) business day following the Date of Grant. Please be aware that if you intend to reject the grant, you should do so immediately after the Date of Grant to avoid potential Section 16 liability. Please advise Dennis Edge and Kim Wolford immediately by e-mail, fax or telephone if you intend to reject this grant. Absent such notice of rejection, the Company will prepare and file the required Form 4 on your behalf within the required two (2) business-day deadline.

If you are currently subject to these requirements, you will have already been advised of your status. If you become a Section 16 insider at some future date, reporting will be required in the same manner noted above.

Other Information

Neither the action of the Company in establishing the Plan, nor any provision of the Plan, nor any action taken by the Company, your employer, the Committee or the Board of Directors under the Plan, nor any provision of this Agreement shall be construed as giving to you the right to be retained in the employ of the Company or any of its subsidiaries or affiliates.

This award is intended to comply with or be exempt from Section 409A of the Internal Revenue Code of 1986, as amended (“Section 409A”), and ambiguous provisions, if any, shall be construed in a manner that is compliant with or exempt from the application of Section 409A, as appropriate.

Exhibit A

POLICY NO. 1405-003 — EFFECTIVE DATE: 08/02/13

Interpretation Contact for the above policy is the Senior Vice President, Chief Administration Officer and Senior Vice President, General Counsel and Corporate Secretary.