Mark Lundy's final bid to overturn his convictions for murdering his wife and daughter has been unanimously declined by the Supreme Court.

Lundy was previously convicted of killing wife Christine 38, and 7-year-old daughter Amber at their Palmerston North home in August 2000.

This morning's Supreme Court judgement is the last in a long string of appeals.

The appeal bid hung on a single point - whether the Court of Appeal was wrong in choosing not to overturn Lundy's convictions when part of the evidence used to secure them was found to be inadmissible.

Lundy's lawyer Jonathan Eaton QC, criticised the use of mRNA evidence at an earlier hearing, calling it "novel and junk science".

The evidence was used to tell the jury the brain or spinal tissue found in tiny specks on Lundy's shirt was likely human, rather than from an animal.

The method for analysing the brain tissue had "never been used before, never been used again", and the evidence based off it had been found inadmissible by an earlier court ruling.

"The name Mark Lundy has become synonymous with flawed expert opinion, flawed science and miscarriage of justice," Eaton said.

The Crown dug up the mRNA evidence after the Privy Council decision to "fill a gap" in the science linking Lundy to the murders, he said.

"Once you've got the link that it's human, it's game over."

Christine and Amber Lundy were found hacked to death at their home, likely with an axe or tomahawk. The murder weapon was never found.

On the night of their murders Lundy had checked into a motel in Petone where he called an escort about 11.30pm.

\It was fiercely contested during his first trial whether or not it was physically possible for Lundy to have travelled between Wellington and his family home in a time that would have allowed him to be in the house at the time of the murders.

Justice Mark O'Regan read out the Supreme Court judgement this morning in Wellington. He said the panel of judges on the case all agreed to dismiss the appeal.

The court cases

Lundy was first convicted of the murders in 2002, and his first appeal attempt resulted in the court increasing the non-parole period of his life sentence to 20 years.

His conviction was quashed by the Privy Council in 2013, which ruled there were problems with the analysis of the brain tissue found on Lundy's shirt, as well as with the time of death.

In a 2015 retrial at the High Court in Wellington, Lundy was again convicted of the murders.

He appealed to the Court of Appeal last year, which found the evidence around the brain tissue should not have been presented to the jury, but decided to uphold the convictions anyway.

The Crown argued Christine Lundy's brain tissue was found on the polo shirt her husband wore on the night of the murders.

Tiny spots consistent with dried blood were also found on the shirt, which were found to contain Amber's DNA.