A square scribbled on a yellowed piece of paper by Renaissance genius Michelangelo sold for $201,600 —  33 times its estimated value, auction house Christie's said Wednesday.

Found stuck to the back of a frame, the small drawing accompanied by a letter from Michelangelo's last direct descendant was initially expected to sell for between $6,000 and $8,000.

But Christie's in New York said the piece went under the hammer for "33.6 times its low estimate," without disclosing any details of the buyer.

The small work depicts a block of marble, with the word "simile," or "similar" in English. It is believed to have been drawn while Michelangelo worked on his famed Sistine Chapel ceiling, a Christie's specialist told AFP in January.

The drawing is coupled with a letter written by Cosimo Buonarroti in 1836, in which he offers the piece by his "illustrious forefather Michelangelo" to Sir John Bowring, the future governor of Hong Kong, whose signature appears at the bottom of the sheet.

Christie's specialists found the letter and diagram attached to the back of a different drawing that had been in a private collection for decades, the auction house said in a media statement. 

Though unsigned by Michelangelo, Christie's said that research confirmed the great Italian artist was responsible for the small drawing.

Fewer than 10 of Michelangelo's works are thought to be privately owned, according to Christie's, with most housed in the Casa Buonarroti, a museum in Florence, Italy.