The Supreme Court has granted Mark Lundy leave to appeal his double murder convictions.
Lundy has been convicted twice of the murders of his then-wife Christine and seven-year-old daughter Amber.
In August 2000 their bodies were found bludgeoned, with multiple wounds, at their Palmerston North home.
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The first conviction came in 2002, before the Privy Council overturned his conviction in 2013. He was found guilty again in a retrial in 2015.
At issue is spots of what is believed to be human brain or central nervous system tissue found on a polo shirt believed to have been worn by Lundy on the night of the murders.
During his second trial, the Crown produced mRNA evidence relating to the stains showing they came from a human source.
In 2018, the Court of Appeal found the evidence around the brain tissue should not have been presented to the jury, but still upheld his convictions based on a finding that no substantial miscarriage of justice had occurred.
His lawyers appealed to the Supreme Court, arguing the Court of Appeal was wrong to uphold the convictions.
Jonathan Eaton QC told the court "the assessment of inevitable guilt was flawed".
"The approach in terms of trial fairness is flawed and the Court of Appeal have conflated factor one, applying the proviso, is guilt inevitable and factor two, notwithstanding, is the trial fair," he argued in court.
On Monday, the Supreme Court agreed to hear the appeal on whether the Court of Appeal erred in its use of the "proviso", which allowed it to dismiss Lundy's case even though some of the evidence was inadmissible.
However it dismissed leave to appeal on two other points, including his behaviour at his wife and daughter's funeral. This refers to Lundy's much-publicised funeral behaviour, where he was photographed collapsing in supposed grief.
"We see no appearance of a miscarriage in the way the Court of Appeal addressed the issue in relation to the applicant's demeanour at the funeral of the deceased," the decision said.
Lundy has always maintained his innocence and that he was away on business in Petone at the time of the murders.