Exhibit 10.31

LETTER AGREEMENT NO. 4

As of March 5, 2010

United
Air Lines, Inc.

77 West Wacker Drive

Chicago, Illinois 60601

[CONFIDENTIAL
MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT]

Dear Ladies and Gentlemen,

United Air Lines, Inc. (the Buyer), and AIRBUS S.A.S. (the Seller), have entered into an Airbus A350-900XWB Purchase
Agreement dated as of even date herewith (the Agreement), which covers, among other things, the sale by the Seller and the purchase by the Buyer of certain Aircraft, under the terms and conditions set forth in said Agreement. The Buyer
and the Seller have agreed to set forth in this Letter Agreement No. 4 (the Letter Agreement) certain additional terms and conditions regarding the sale of the Aircraft. Capitalized terms used herein and not otherwise defined in
this Letter Agreement will have the meanings assigned thereto in the Agreement. The terms herein, hereof and hereunder and words of similar import refer to this Letter Agreement.

Both parties agree that this Letter Agreement will constitute an integral, nonseverable part of said Agreement, that the provisions of said Agreement are
hereby incorporated herein by reference, and that this Letter Agreement will be governed by the provisions of said Agreement, except that if the Agreement and this Letter Agreement have specific provisions which are inconsistent, the specific
provisions contained in this Letter Agreement will govern.



AIRBUS S.A.S. & UNITED AIR LINES, INC.  PROPRIETARY AND CONFIDENTIAL



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|1. | DEFINITIONS
|-- | -----------

[CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT].

A350-900XWB Aircraft  any or all of the twenty-five (25) firm A350-900XWB aircraft for which the delivery schedule is set
forth in Clause 9.1 to this Agreement and any firmly ordered A350-900XWB aircraft with respect to which the Buyer has exercised a Purchase Right, to be sold by the Seller and purchased by the Buyer pursuant to this Agreement, together with all
components, equipment, parts and accessories installed in or on such aircraft [CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT].

Aircraft  as applicable, (i) any or all of the A350-900XWB Aircraft sold or to be sold by the Seller and purchased or to be
purchased by the Buyer pursuant to this Agreement, and (ii) any or all of the A350XWB Aircraft with respect to which the Buyer has exercised a Purchase Right, [CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST
FOR CONFIDENTIAL TREATMENT].

A350XWB Purchase Right Aircraft  up to fifty (50) A350XWB aircraft
[CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT] with respect to which the Buyer has exercised a Purchase Right.

Purchase Right  as defined in Paragraph 2.1 of this Letter Agreement No. 4.

[CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT].



|2. | A350XWB PURCHASE RIGHT AIRCRAFT
|-- | -------------------------------



|2.1. | A350XWB Purchase Right Aircraft
|---- | -------------------------------

The Seller grants the Buyer the right to purchase the A350XWB Purchase Right Aircraft on the commercial terms offered in the Agreement for
the A350-900XWB Aircraft, except where specifically stated otherwise (the Purchase Right).

[CONFIDENTIAL
MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT].



|2.2. | Purchase Right Exercise
|---- | -----------------------

The Buyer will exercise its Purchase Rights as follows:



| | (i) | The Buyer will notify the Seller of its desire to purchase each A350XWB Purchase Right Aircraft by sending a written notice to the Seller, no later than
[CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT].
| | --- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------



AIRBUS S.A.S. & UNITED AIR LINES, INC.  PROPRIETARY AND CONFIDENTIAL



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|2.3. | A350XWB Purchase Right Aircraft Predelivery Payments
|---- | ----------------------------------------------------

[CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT].



|3. | [CONFIDENTIAL MATERIAL FROM PAGES LA4-9 TO LA4-20 OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT].
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|4. | [CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT]
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|5. | [CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT]
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|6. | [CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT]
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|7. | ASSIGNMENT
|-- | ----------

This Letter
Agreement and the rights and obligations of the parties will be subject to the provisions of Clause 21 of the Agreement.



|8. | CONFIDENTIALITY
|-- | ---------------

This
Letter Agreement is subject to the terms and conditions of Clause 22.10 of the Agreement.



|9. | COUNTERPARTS
|-- | ------------

This Letter
Agreement may be executed by the parties hereto in separate counterparts, each of which when so executed and delivered shall be an original, but all such counterparts shall together constitute one and the same instrument.



AIRBUS S.A.S. & UNITED AIR LINES, INC.  PROPRIETARY AND CONFIDENTIAL



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If the foregoing correctly sets forth our understanding, please execute the original and one (1) copy hereof
in the space provided below and return a copy to the Seller.



Very truly yours,AIRBUS S.A.S.By:

/s/ John J. LeahyIts:

Chief Operating OfficerCustomers




| |  |                        |  |                             
| |  | ---------------------- |  | ----------------------------
| |  | Accepted and Agreed   
| |  | UNITED AIR LINES, INC.
| |  |                       
| |  | By:                    |  | /s/ Kathryn A. Mikells      
| |  |                       
| |  | Its:                   |  | Executive Vice President and
| |  |                        |  | Chief Financial Officer     



AIRBUS S.A.S. & UNITED AIR LINES, INC.  PROPRIETARY AND CONFIDENTIAL



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EXHIBIT A-1

A350-800XWB BASIC AIRCRAFT DESCRIPTION DOCUMENT

The A350-800XWB Basic Aircraft Description Document is contained in a separate folder.



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EXHIBIT B-1 to LA-4

[CONFIDENTIAL MATERIAL OMITTED AND FILED SEPARATELY WITH THE SEC PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT]



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EXHIBIT B-2 TO LA-4

[CONFIDENTIAL MATERIAL OMITTED

AND FILED SEPARATELY WITH THE SEC

PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENT]