Before he left Microsoft in 1983, Allen claims Gates attempted to buy his shares from him at a bargain price.
"It's not fair that you keep your stake in the company," Allen reports Gates as saying, making what Allen described as a "lowball" offer of $US5 a share for his stock. Allen says he wouldn't go below $US10. As a result, Allen says he kept his share.
"As it turned out, Bill's conservatism worked to my advantage. If he'd been willing to offer something close to my asking price, I would have sold way too soon," says Allen in the book.
Gates, who has recently been traveling in India working on his own philanthropy projects, did not directly contest Allen's account, but sought to play down friction.
"While my recollection of many of these events may differ from Paul's, I value his friendship and the important contributions he made to the world of technology and at Microsoft," Gates said in an emailed statement.
A Microsoft spokesman declined to comment.
Allen is ranked the 57th richest person in the world with a fortune of $US13 billion, according to Forbes magazine, largely due to his Microsoft holdings. Gates is ranked No. 2 with $US56 billion.
Allen's book, titled Idea Man, is set to be published later this month by Portfolio.
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