Exhibit 99.1

Press Release

WMI Holdings Corp. Appoints New Chief Accounting Officer

SEATTLE, June 4, 2012 – WMI Holdings Corp., (Pink Sheets: WMIH.PK) (the “Company”), formerly Washington Mutual, Inc., today announced that Timothy Jaeger has been named Interim Chief Accounting Officer of the Company, effective May 28, 2012. Mr. Jaeger, who is a principal of CXO Consulting Group, LLC, has been retained through an Engagement Agreement entered into between the Company and CXO.

Charles Edward Smith, Interim Chief Executive Officer, stated, “We are pleased to add Timothy Jaeger as Interim Chief Accounting Officer. Tim brings broad accounting experience in a number of cross-industry contexts, including public and private companies as well as venture capital and corporate acquisitions. We look forward to working closely with him.”

Mr. Jaeger, age 53, is a Certified Public Accountant with over 25 years of accounting experience. Most recently, from December 2006 to March 2012, Mr. Jaeger served as Senior Vice President-Chief Accounting Officer/CFO of Macqurie AirFinance, Ltd., a global aviation lessor providing aircraft and capital to the world’s airlines. From November 2006 to December 2009, Mr. Jaeger was a partner of Tatum Partners, LLC, an executive services and consulting firm in the U.S. From June 2005 to October 2006, Mr. Jaeger, serving as principal of CXO Consulting Group, LLC, was Interim Controller/Sarbanes Oxley Coordinator at ICON Estates/Robert Mondavi Winery/Constellation Brands.

About WMI Holdings

WMI Holdings Corp., formerly Washington Mutual, Inc., consists primarily of WM Mortgage Reinsurance Company, Inc. (“WMMRC”), a wholly owned subsidiary of WMI that is incorporated in Hawaii. The primary business of WMI Holdings is a legacy reinsurance business that is currently operated in runoff mode by WMMRC.

Cautionary Statement Regarding Forward-Looking Statements

This press release contains certain statements that may be deemed to be forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. Such forward-looking statements are based on the Company’s current plans, expectations, estimates and management’s beliefs about the Company’s future performance. Words such as “anticipates,” “expects,” “intends,” “plans,” “believes,” “seeks,” “estimates” or variations of such words and similar expressions are intended to identify such forward-looking statements. These statements are not guarantees of future performance and are subject to risks and uncertainties that are difficult to predict and which may cause the Company’s actual results and performance to differ materially from those expressed or forecasted in any such forward-looking statements. These risks include, among other factors, changes in business, economic and market conditions, changes in government regulation, and changes in the competitive environment in which the Company operates. Some of the specific risks that are associated with the Company include, but are not limited to, the following: (i) the Company does not currently intend to have any of its securities listed on an exchange or a national market and, therefore, its common stock may have less liquidity than exchange-traded securities; (ii) transfers of the common stock of the Company are and will continue to be subject to certain transfer restrictions as set forth in the Articles and Bylaws; (iii) there is no guarantee that the Company will be able to successfully utilize the net operating losses that will be

retained by the Company; and (iv) the Company may need to seek regulatory approval from the Hawaii State Insurance Commissioner from time to time with respect to certain aspects of WM Mortgage Reinsurance Company, Inc.’s operations. However, readers should carefully review the statements set forth in the reports, which the Company has filed or will file from time to time with the Securities and Exchange Commission.

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Contact

Andrew Siegel / Jed Repko / Aaron Palash

Joele Frank, Wilkinson Brimmer Katcher

(212) 355-4449

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