Mark Lundy's case has again reached the Supreme Court, where he is challenging his convictions for murdering his wife and daughter.

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

The latest in a long string of appeals will focus on "novel and junk science" used to analyse brain tissue at the scene, which Lundy's lawyer criticised in an earlier hearing.

Lawyer Jonathan Eaton, QC, said Lundy referred to himself as being a "guinea pig through the justice system".

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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.

Tomorrow he will be arguing the convictions should have been overturned due to this finding.

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

Mark Lundy being supported after the funeral of his wife Christine and daughter Amber in 2000. Photo / Mark Mitchell
Mark Lundy being supported after the funeral of his wife Christine and daughter Amber in 2000. Photo / Mark Mitchell

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.

Lundy was first convicted of their 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.

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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.

The hearing in Wellington is set down for one day.