An appeals court in Portugal has overturned the libel conviction of a former Portuguese detective who published a book alleging the parents of Madeleine McCann were involved in their daughter's disappearance, their lawyer said.

Lisbon lawyer Isabel Duarte said she was notified of the court's decision to uphold Goncalo Amaral's appeal against the order to pay Kate and Gerry McCann 500,000 euro (£395,000) in compensation.

That ruling was handed down by a lower court in Lisbon a year ago, prompting Mr Amaral to appeal.

Ms Duarte said she intended to fight the decision at the Supreme Court.

Mr Amaral was part of the police investigation into Madeleine's disappearance from a holiday home in Portugal's Algarve region in May 2007, days before her fourth birthday.

In 2008 he published his book about the case called The Truth Of The Lie.

The McCanns sought 1.2 million euro (£948,000) in damages from Mr Amaral, saying they were "totally destroyed" and "depressed" by his allegations and felt "ashamed" that they might appear to have been to blame for their daughter's disappearance.

Mr Amaral had argued in his defence that his claims stemmed from the police investigation and that Portuguese media had already reported the possibility that the parents might have played a role in Madeleine's disappearance.

The appeals court "decided that (Mr Amaral) had the right to do what he did. It said he can write what he wants", Ms Duarte said. "It absolved him, said he didn't have to pay anything."

She said the McCanns took the reversal in their stride after a long time battling in Portuguese courts.

"They're used to it," Ms Duarte said.

Portuguese police closed the case in 2008 because authorities had detected no crime, but British police are still looking into it.

Madeleine would turn 13 next month.