A friend of Christine Lundy said the latest appeal would be devastating for Christine's friends and family.
Although it was not yet clear precisely what evidence would be contested in an upcoming appeal, ribonucleic acid (RNA) was discussed during the most recent trial.
A key plank of the Crown's case was that Christine Lundy's brain matter was found in one of her husband's polo shirts.
According to prosecutor Philip Morgan, QC, testing showed two stains found on the shirt were from tissue one billion, billion times more likely to belong to Christine Lundy than any other person in New Zealand.
Dr Laetitia Sijen from the Netherlands Forensic Institute told the court she arrived at a conclusion brain matter was present on Lundy's shirt based on tests performed on RNA in a sample.
RNA indicated which part of the body cells came from and was different to DNA, which revealed who cells belonged to.
Professor of molecular medicine Stephen Buston, from Angela Ruskin University in Cambridge, UK, told the jury Dr Sijen did not follow written instructions when conducting tests on the sample.
He claimed there were problems with timings and the test.
"The method they are using for the detection of RNA is not really fit for purpose," he said in court. "I would be highly reluctant to accept the results ... because of the technique that has been applied."
Some of Lundy's relatives were made aware of the appeal before Ms Kincade announced it to media this afternoon.
Lundy's sister-in-law Andrea and his brother-in-law Dave Jones knew about the appeal but declined to comment this afternoon.
Lundy was first found guilty of the murders in 2002 and sentenced to life in jail with a minimum non-parole term of 17 years.
He appealed that year. The appeal failed. A judge added three more years to Lundy's non-parole term.
At the time, it was the longest non-parole period of imprisonment for a life sentence ever handed down in New Zealand.
In 2013, Lundy appealed to the Privy Council, which threw out his conviction and a retrial began on February 8 this year.