Uber Technologies Inc.’s ousted chief executive, Travis Kalanick, is appointing two new directors to the ride-hailing firm’s board, a surprise move that would bolster his clout as the company faces several critical decisions including a possible multibillion-dollar investment from SoftBank Group Corp.

Mr. Kalanick appointed former Xerox Corp. CEO Ursula Burns and former CIT Group Inc. CEO John Thain as the 10th and 11th Uber directors, effective Friday, according to a statement from him to The Wall Street Journal.

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