General Motors Corp. and Tracinda Corp., the investment company owned by billionaire Kirk Kerkorian, issued a joint statement late yesterday saying the two sides could not reach an agreement that would place a Kerkorian adviser on GM's board of directors.

Tracinda owns 9.9 percent of GM's outstanding shares, making Kerkorian GM's largest individual shareholder. In the statement, GM and Tracinda said the companies had "constructive discussions" but could not agree to put Jerome B. York on the GM board.

York, a former chief financial officer at International Business Machines Corp., was Kerkorian's key assistant when the investor clashed with Chrysler Corp. in the 1990s.

Earlier this week, GM confirmed that the automaker was talking with Tracinda about board representation for Kerkorian. The two sides will continue to discuss the matter, the statement said.

GM directors and chief executive G. Richard Wagoner Jr. are trying to get the No. 1 automaker back on track after a year of substantial slides in profit and loss of U.S. market share.

Analysts and industry observers have questioned Wagoner's stewardship of the company and criticized his turnaround plans for the giant automaker as insufficient, given GM's many problems. Wagoner plans to cut 30,000 jobs at GM and close several factories that build poorly selling vehicles.

Kerkorian has a history of taking substantial positions in companies and prodding management to make changes. So far, his buildup of GM shares has been a sour investment. The shares have fallen more than 25 percent since September.