Apple Corp claimed that Apple Computer was in breach of an earlier agreement not to sell music using the apple logo. It was the latest round in a long history of conflict between the two companies.
"I find that no breach of the trademark agreement has been demonstrated," Justice Edward Mann said in his judgement, issued in London's High Court. "The action therefore fails."
The current case hinged on a confidential out-of-court settlement in 1991 that set out strict fields of business for both companies.
Apple Computer agreed not to go into the physical music business, i.e. selling CDs and DVDs, using its distinctive logo. But the agreement did not cover other forms of music transmission, since at that time the internet was not considered.
"It's an interesting case," said Conan Chitham, an independent intellectual property lawyer from law firm Mishcon de Reya.
"Apple Corporation had a bit of running to do to convince the judge that CDs and digital downloads are the same thing, and the judge took a very savvy decision that they are not the same thing.
"It's a good example of a little clause in an old contract turning round and biting you."
Apple Computer ran into trouble almost immediately after deciding on its logo in 1976.
Barely two years later Apple Corporation, owned by Paul McCartney, Ringo Starr, John Lennon's widow Yoko Ono and the estate of George Harrison, sued the company and settled in 1981 for an undisclosed sum and an agreement to stay out of the music business.
But in 1986 Apple, like other computer manufacturers, started to integrate sound into their computers. Apple Corporation sued again in 1989, severely hampering development of the Apple II line, and the case was settled in 1991 for around $26.5m.
Apple Computer hit back in a low key way with one of its first sounds.
Engineer Jim Reekes created a system sound for Apple called 'Sosumi' (pronounced
'So, sue me').
Finally in 2003, after the huge success of the iPod and iTunes service, Apple Corporation sued again.
Today the judge gave Apple Corporation leave to appeal the decision, and further action looks inevitable. "For them it's personal," said Chitham.
Latest Tesla news: Tesla stock price tanks amid reports of 'widening probe' by SEC and claims the base Model 3 loses money
SEC 'probe' takes its toll on Tesla as new research suggests that Tesla loses $6,000 on every $35,000 Model 3
10nm Cannon Lake Core i3-8121U CPUs make a rare outing with Intel's NUC mini PC
'Notorious' Australian child hacker thought he had executed 'flawless' hack
The former employee says that Tesla fired him for bringing the accusations to management internally