The U.S. government plans to sell another 30 million shares of General Motors stock in a public offering today as it speeds up efforts to divest itself from a stake in the auto giant that it got in a bailout four years ago.

The Treasury Department will set the price for the shares after the markets close today, with the sale taking place shortly thereafter. A United Auto Workers retiree health care trust fund will join the sale and sell 20 million shares, pushing the size of the offering to 50 million shares.

General Motors Co. stock fell 76 cents, or 2.2 percent, to $34.20 in Wednesday afternoon trading, but it has seen huge growth recently. The stock hit $35.49 Tuesday, the highest point since December of 2010, according to FactSet. Shares are up about 19 percent since the beginning of the year.

The public offering will help accelerate the government’s exit from owning GM stock, which it got in exchange for a $49.5 billion bailout in 2008 and 2009. Late last year the government still owned 500 million shares of the automaker, but GM bought 200 million shares for $5.5 billion in December, and the Treasury pledged to gradually sell its remaining stake by early next year.

GM has longed for the government to exit partial ownership of the company, hoping to shed the derisive nickname “Government Motors,” as well as attract customers who have shunned GM cars because it took government money. GM nearly ran out of cash late in 2008 and needed the government cash to make it through bankruptcy protection. While under government ownership, the company also falls under executive pay caps that it says hinder recruiting of top talent.

The sale of 50 million shares, conducted by Citigroup Global Markets Inc., J.P. Morgan Securities LLC and Morgan Stanley & Co. LLC, will coincide with GM’s re-entry into the Standard & Poor’s 500 index.

Today, GM will replace H. J. Heinz Co. in the S&P 100 and 500 indices. The ketchup maker’s acquisition by 3G Capital and Warren Buffett’s Berkshire Hathaway is expected to be complete by then.

Stocks often get at least a temporary boost after joining the S&P 500 because funds that follow the index have to add the shares to their portfolios.

GM Chief Financial Officer Dan Ammann said in a statement that the company appreciates the chance to help with the sale, which was made possible by rejoining the S&P 500.

At the end of April, the latest report available, Treasury had recovered about $30.7 billion of the $49.5 billion bailout. That means that taxpayers are still $18.8 billion in the hole. So far this year, government has sold 58.4 million shares of GM stock and earned net proceeds of $1.6 billion. That left 241.7 million shares of GM stock still in government hands. That stock would have to sell for about $78 per share for the government to recoup its total bailout costs.

After today’s sale, the government would still own about 211 million shares, although it likely sold additional shares on the open market in May that haven’t been disclosed yet. The Treasury Department said it still plans to sell its entire stake in GM by early next year.