The men behind the site were convicted in April after it was ruled their site encouraged copyright infringement. The men now all face jail terms and could be looking at large claims for damages.
Legal representatives for The Pirate Bay website requested a new trial after it was discovered a judge in the case was a member of some copyright protection groups.
It was ruled that the judge being a member of such groups did not influence the outcome of the case.
The Svea Court of Appeal did say that the judge involved should have said that he was a member of the copyright groups before the case went to court.
A statement issued by the court said:
"The fact that he failed to shed light on this does not however mean that there was any wrongdoing during the proceedings that would require a retrial
"This was not a case of bias,"
This decision can now not be appealed.
The Pirate Bay website listed details of websites where people could access pirated movies,music, TV programmes and software.
In their defense the four men said they were not in breach of copyright because they didn't store the material themselves.
The court found against them because they ruled that they continued to offer the service after they knew visitors to the site were being directed to pirated material.