Exhibit 10.4

SHARE UNIT AWARD NOTICE

Share Unit Award Notice under the United Continental Holdings, Inc. 2006 Director Equity Incentive Plan, as amended (the “Plan”) dated as of                     , between United Continental Holdings, Inc., a Delaware corporation (the “Company”), and                     .

This Share Unit Award Notice (the “Award Notice”) sets forth the terms and conditions of an award of                      share units (the “Award”) that are subject to the terms and conditions specified herein (“Share Units”) and that are granted to you under the Plan. This award constitutes an unfunded and unsecured promise of the Company to deliver (or cause to be delivered to you), subject to the terms of this Award Notice, a cash payment for each Share Unit as set forth in Section 3 below.

SECTION 1. The Plan. This Award is made pursuant to the Plan, all the terms of which are hereby incorporated in this Award Notice. In the event of any conflict between the terms of the Plan and the terms of this Award Notice, the terms of the Plan shall govern.

SECTION 2. Definitions. Capitalized terms used in this Award Notice that are not defined in this Award Notice have the meanings as used or defined in the Plan.

SECTION 3. Delivery of Cash Pursuant to Settlement of Share Units. Your rights to the Share Units vest in accordance with the terms established by the Board on the date of grant. This award vests on [insert vesting date or schedule] (the “Vesting Date”). The Share Units, including any Share Units credited to your Share Account for dividends in accordance with Section 6(d)(ii) of the Plan, shall be settled in cash. On the Vesting Date, you shall receive a lump sum cash payment equal to the Market Price of a Share on the Vesting Date multiplied by the number of Share Units (including any fraction thereof) that vest on such Vesting Date. Upon settlement, the Share Units shall be extinguished and such number of Share Units will no longer be considered to be held by you for any purpose.

SECTION 4. Voting Rights; Dividends. You do not have any of the rights of a stockholder with respect to the Share Units granted to you pursuant to this Award Notice. Your Share Account will be credited with additional Share Units as of the date on which dividends, if any, are paid, in accordance with Section 6(d)(ii) of the Plan.

SECTION 5. Successors and Assigns of the Company. The terms and conditions of this Award Notice shall be binding upon and shall inure to the benefit of the Company and its successors and assigns.

SECTION 6. Committee Discretion. The Committee shall have full and plenary discretion with respect to any actions to be taken or determinations to be made in connection with this Award Notice, and its determinations shall be final, binding and conclusive.

SECTION 7. Amendment of this Award Notice. The Committee may waive any conditions or rights under, amend any terms of, or alter, suspend, discontinue, cancel or terminate this Award Notice prospectively or retroactively; provided, however, that, except as set

forth in Section 15 of the Plan, any such waiver, amendment, alteration, suspension, discontinuance, cancelation or termination that would materially and adversely impair your rights under this Award Notice shall not to that extent be effective without your consent (it being understood, notwithstanding the foregoing proviso, that this Award Notice and the Share Units shall be subject to the provisions of Section 3(c) of the Plan).