Listen: Lost Kurt Cobain cover of the Beatles' 'And I Love Her' surfaces

Just when you think there's no more great Kurt Cobain material in the vault, another piece of audio surfaces. This time, it's a cover of the Beatles' “And I Love Her,” which the late Nirvana singer apparently recorded years ago on a cassette tape.

Brett Morgen, who directed the upcoming documentary Kurt Cobain: Montage of Heck, sorted through old Cobain tapes while putting together the movie. One of his best discoveries was Cobain softly singing the 1964 tune that originally appeared on A Hard Day's Night. Despite its cheerful lyrics, the original recording carried a somber tone built around acoustic guitars.

So what does Kurt's recording sound like? Pretty much what you'd expect. It's an abbreviated version, and it takes a more grunge vibe with a slowed-down tempo and slightly mumbled vocals.

“Nobody in Kurt's life — not his management, wife, bandmates — had ever heard his Beatles thing," Morgen told Rolling Stone, which broke the story. “I found it on a random tape. It's a Paul song. How's that for shattering the myth?”

The myth Morgen refers to is the notion that Cobain wasn't a fan of Paul McCartney, who wrote “And I Love Her.” Cobain had previously said that while he liked the Beatles, he hated McCartney. Evidently, that was a bit of an exaggeration.

Cobain's rendition of “And I Love Her” will be included on the score to the documentary, along with plenty of other unreleased Cobain music that Morgen found in the archives. A trailer for the movie features footage of Cobain as a toddler and pictures of writing from his journals.

Morgen has been working for nearly eight years on the film, which has the blessing of Cobain's widow, Courtney Love. The movie has earned rave reviews from critics and viewers at the Sundance Film Festival and the Berlin International Film Festival. The movie, which RS calls “the most intimate rock doc ever,” can be seen by U.S. viewers on HBO on May 4.

The revelation that Cobain recorded a McCartney song should be good news for Sir Paul, who has performed with the surviving members of Nirvana a few times in recent years. McCartney joined Dave Grohl, Krist Novoselic, and Pat Smear to record “Cut Me Some Slack,” which ended up winning a Grammy Award for Best Rock Song.