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

Exhibit 10.40.2

SECOND AMENDMENT TO

UNITED CONTINENTAL HOLDINGS, INC.

LONG-TERM RELATIVE PERFORMANCE PROGRAM

WHEREAS, the United Continental Holdings, Inc. Long-Term Relative Performance Program, as amended (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, 2014:

1. Subject to further adjustment as set forth in the Program, the Committee confirms that, as of January 1, 2014, the Industry Group consists of Alaska Air Group, Inc., American Airlines Group, Inc., Delta Air Lines, Inc., Southwest Airlines Co., and JetBlue Airways Corporation.

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

“(s) “Industry Pre-tax Margin” with respect to a Performance Period means, as established by the Committee within 90 days after the first day of the Performance Period (but in no event after the date required for a performance goal to be considered pre-established under section 162(m) of the Code), either:

If the fiscal year of a company in the Industry Group is not the calendar year, then such company’s cumulative revenues for a Performance Period shall be determined based upon the fiscal quarters of such company that coincide with the fiscal quarters contained in such Performance Period.”

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

“(z) “Pre-tax Margin” with respect to the Company and with respect to a Performance Period means, as established by the Committee within 90 days after the first day of the Performance Period (but in no event after the date required for a performance goal to be considered pre-established under section 162(m) of the Code), either:

(A) the cumulative Pre-tax Income for the Company for such Performance Period divided by the Company’s cumulative revenues (determined on a consolidated basis based on the regularly prepared and publicly available statements of operations of the Company prepared in accordance with applicable accounting rules) over such Performance Period; provided, however, that, such cumulative revenues shall be adjusted to exclude any item determined to be special, extraordinary or unusual in nature or infrequent in occurrence as determined by the Committee in accordance with applicable accounting rules; or

(B) (i) the percentage determined under clause (A) above, minus (ii) the percentage determined by dividing (a) the cumulative Pre-tax Income of the Company for the calendar year immediately preceding the first day of such Performance Period by (b) the Company’s cumulative revenues (determined as provided in clause (A) above) over such calendar year (with the calculation in this clause (B) representing the Company’s average Pre-tax Margin change over the Performance Period).”

4. Sections 2.1((i), 2.1(p), 2.1(ff) and 2.1(ii) shall each be amended to delete the clause at the end of each such sections which begins with “which shall be expressed as”.

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

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