Today Mr Justice Edward Mann ruled that the computer firm used the apple logo in association with its store, not the music, so no breach was present.
The Beatles' label had wanted the High Court to award damages and stop Apple Computer form using the logo on its iTunes Music Store.
During the case last month lawyers defending the Beatles' record label had gone through the process of buying a song on the iTunes Music Store to show how much the logo was used.
[Update] As more details of the case are revealed it appears that Apple Corps intends to appeal the decision made today in London.
The BBC has ongoing coverage, but of interest it has now published some quotes from the Judges deliberation on the case:
The iPod and iTunes do not breach the trademark because they are merely ways of conveying music and nothing to do with the creation of the music itself, Mr Justice Edward Mann ruled at London's High Court.
Mr Justice Mann said iTunes was "a form of electronic shop" and the presence of the Apple Computer logo on the service did not suggest "a relevant connection with the creative work".
In considering this latest development, High Court judge Mr Justice Mann said the new clash followed shortcomings in Apple Corps and Apple Computer's 1991 agreement.
He said: "If their intention... was to create obscurity and difficulty for lawyers to debate in future years, they have succeeded handsomely."
[Update 2] The full judgement is now available in PDF format.