New York (CNN Business) Elon Musk will buy another $20 million of Tesla stock with his own money, covering the cost of the fine the company has to pay for his tweets.

Musk and Tesla each agreed last month to pay $20 million to settle a federal lawsuit. The SEC alleged Musk misled investors when he tweeted on August 7 that he had " funding secured " to take Tesla private.

As part of the SEC settlement , Musk also agreed to give up his position as chairman of Tesla, although he will remain CEO. The company will add new independent board members and have greater oversight of Musk's communications with the public.

The settlement was approved by a federal judge late Monday.

Musk's share purchase is unusual -- for CEOs, not for him. Most executives do not spend their own money to buy shares of their companies' stocks at market price. But Musk also purchased shares with his own cash in May and June

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