Exhibit 10.33

LETTER AGREEMENT NO. 6

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. 6 (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. | A350XWB AIRCRAFT DEFINITION
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|6. | ASSIGNMENT
|-- | ----------

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



|7. | CONFIDENTIALITY
|-- | ---------------

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



|8. | 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