FIRST AMENDMENT TO UNITED CONTINENTAL HOLDINGS, INC. LONG-TERM RELATIVE PERFORMANCE PROGRAM

Exhibit 10.49

FIRST AMENDMENT TO

UNITED CONTINENTAL HOLDINGS, INC.

LONG-TERM RELATIVE PERFORMANCE PROGRAM

WHEREAS, the United Continental Holdings, Inc. Long-Term Relative Performance Program (the “Program”) has heretofore been adopted by the Compensation Committee (the “Committee”) of the Board of Directors of United Continental Holdings, Inc. to implement in part the Performance Award provisions of the United Continental Holdings, Inc. Incentive Plan 2010, as amended from time to time; and

WHEREAS, the Committee is authorized to amend the Program; and

WHEREAS, the Committee desires to amend the Program in certain respects;

NOW, THEREFORE, the Program shall be amended as follows, effective with respect to Performance Periods (as such term is defined in the Program) beginning on or after January 1, 2012:

1. Sections 2.1(d) and 2.1(e) of the Program shall be deleted and the following shall be substituted therefor:

“(d) [Reserved.]

(e) [Reserved.]”

2. The term “Base Amount” shall be deleted from each place such term appears in Sections 2.1(u) and 3.1 of the Program and the term “Target Opportunity” shall be substituted therefor.

3. Section 2.1(v) of the Program shall be deleted and the following shall be substituted therefor:

“(v) “Payout Percentage” means, with respect to each Participant for a Performance Period for which the Performance Target is satisfied, a percentage, determined in accordance with the following table (the Administrator may provide for varying percentages (including through straight line interpolation) between levels) as of the earlier of (i) the last day of such Performance Period, (ii) the date of such Participant’s death or Disability, or (iii) the day immediately preceding the date upon which a Change of Control occurs:

4. The words “(which may be 0%)” shall be deleted from each of Sections 2.1(ee) and 2.1(hh) of the Program.

5. The following new paragraph shall be added to the end of Section 2.1 of the Program:

“(jj) “Target Opportunity” means, with respect to a Participant for a Performance Period, a dollar amount established by the Administrator as the Target Opportunity for such Participant with respect to such Performance Period (which, in the discretion of the Administrator, may be expressed as a percentage of such Participant’s base annual salary payable by the Company or a Subsidiary).”

6. The words “Base Amount Multiple (if other than 100%)” shall be deleted from Section 3.1 of the Program and the term “Target Opportunity” shall be substituted therefor.

7. The term “Base Amount Multiples” shall be deleted from Section 3.2(e) of the Program and the term “Target Opportunities” shall be substituted therefor.

8. The term “Base Amount Multiple” shall be deleted from Section 4.2(c) of the Program and the term “Target Opportunity” shall be substituted therefor.

9. As amended hereby, the Program is specifically ratified and reaffirmed.

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