Yahoo CEO Scott Thompson should resign for lying on his CV about having a computer science degree which he did not have, another major investor in the company has demanded.

Calls for the CEO's firing started last week after Yahoo disclosed that its board is investigating a discrepancy in Thompson's CV. The investigation prompted a very public debate over Thompson's ability to continue to lead the struggling company.

The company has acknowledged that Thompson's CV and the Yahoo's regulatory filings with the US Securities and Exchange Commission overstated his technology background to include a degree in computer science, which he did not have.

The company called it "an inadvertent error."

Some Yahoo investors and industry analysts, however, disagreed with the company's conclusion and have been very vocal in recent days about their desire that Thompson be terminated.

Third Point LLC, one of its largest investors and the source of reports of the discrepancy in Thompson's CV, was the first to pressure the company to make a move.

In a letter to Yahoo's board of directors on May 3, Third Point CEO Daniel Loeb said the company needs to determine if Thompson violated Yahoo's Code of Ethics.

"If Mr. Thompson embellished his academic credentials we think that it 1) undermines his credibility as a technology expert and 2) reflects poorly on the character of the CEO who has been tasked with leading Yahoo! at this critical juncture," wrote Loeb. "Now more than ever, Yahoo investors need a trustworthy CEO."

Eric Jackson of Ironfire Capital, which reportedly owns about 3.2 million Yahoo shares, this weekend said it's time for Thompson, who joined the company early this year, to be replaced.

"I think Thompson's got to go," Jackson told the San Jose Mercury News. "Putting shareholders aside, I don't know how any engineer at Yahoo could listen to that guy from now on and not think in the back of their mind, why in the heck would you make up that you studied computer science?"

Yahoo has not yet made any statements about how its probe into the situation is progressing.

Industry analysts generally agree that Thompson's reign at Yahoo now is tenuous at best. And that could spell trouble for a company that has been trying to regain its footing for the past year or so.

Thompson has been bullish in leading Yahoo for the past few months, overseeing layoffs, the ouster of board members and coming up with a plan to turn the company around.

"The effect on Yahoo will primarily depend on the outcome of the board's inquiry, but the inquiry alone is a distraction to all Yahoo employees," said Patrick Moorhead, an analyst with Moor Insights & Strategy.

"As long as the inquiry lasts, employees and shareholders will have an uncertain future and that never has a positive outcome. This is just one more item that drags down Yahoo and could keep them from staging a comeback and becoming more relevant," Moorhead added.