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Just what was the beef between Dave and Oprah all about, anyway?

David Letterman has finally revealed the origins of his 16-year feud with Oprah Winfrey -- and Uma Thurman has nothing to do with it.

During a Tuesday appearance on The Daily Show with Jon Stewart, Letterman, 63, explained that his frosty relationship with the daytime queen "predates the incident at the Academy Awards." While hosting the 1995 Oscars, Letterman jokingly introduced Uma Thurman to Winfrey, poking fun at their quirky names by repeating "Oprah...Uma. Uma...Oprah."

Instead, Letterman recalled to Jon Stewart, the trouble began around 1989, when he and his girlfriend Regina Lasko (they wed last year) encountered Winfrey and her beau Steadman Graham at a restaurant.

"This is hilarious," Letterman said he told Lasko. "I'm going to make Oprah buy us lunch."

The comic then told his waiter, "'Oh, this woman right over there has been kind enough to take care of our check.'"

As the late-night host departed the eatery, he waved to Winfrey, who waved back -- thus convincing the waiter that she was indeed footing Letterman's lunch tab.

Stewart's response to the tale? "Oh, for f--k's sake!"

Letterman and Winfrey buried the hatchet in 2005 -- parodying the feud in a Super Bowl ad last year.