A final attempt by David Bain to have five charges of murder against him dismissed will be heard in the High Court in Christchurch on Monday morning.
A retrial was ordered by the Privy Council in London in 2007 after it quashed the original murder convictions, saying there had been a miscarriage of justice.
The Bain defence team returned to the Privy Council two months ago to say it had new evidence that should entitle Mr Bain to a stay of proceedings.
The Privy Council said the New Zealand courts should deal with the application, which is being heard on Monday.
Mr Bain is accused of murdering his parents and three siblings in 1994.
The defence team says advances in forensic testing since the original trial in 1995 show there is no case against Mr Bain.
He has already served 12 years of a life sentence. He has been on bail since May 2007.