Apple Computer today announced that the long-running dispute with The Beatles over the use of the Apple trademark has been settled, bringing the possibility of Beatles downloads closer.

The Beatles’ company, which uses a green Granny Smith apple as its trademark, has previously – and unsuccessfully – sued the computer group over the use of the Apple Corps name and logo.

Today’s agreement between Apple Computer and Apple Corps replaces a 1991 agreement that gave Apple Computer ownership of all trademarks related to “Apple”. Now Apple Computer will now license specific trademarks back to the Beatles’ Apple Corps for the music company’s use.

“We love the Beatles,” said Apple’ Computer’s CEO Steve Jobs said. “It has been painful being at odds with them over these trademarks.”

Manager of Apple Corps Neil Aspinall is also pleased that the dispute is over: “The years ahead are going to be very exciting times for us. We wish Apple Inc. every success and look forward to many years of peaceful co-operation with them.”

The settlement raises the tantalising possibility that the Fab Four’s songs may soon be made available for users to download on Apple’s iTunes store – the biggest music download site in the world. Currently, the Beatles’ peerless back catalogue is not available in mp3 form on any download site.

But nothing is confirmed yet: despite the fact that an Apple spokeswoman was keen to stress the new-found “co-operation” between the two companies, no statement regarding the digitisation of the Fabs songs has been issued.

But if the Beatles catalogue does end up on iTunes, the band could become chart-toppers once more. The Fabs racked up a mammoth 17 No 1 singles between 1962 and 1969. Who would bet against them getting another?