The Court of Appeal has dismissed Mark Lundy's appeal against his conviction for the murder of his wife and daughter.

The appeal was the latest in a long-running legal saga, since Christine and Amber Lundy were found brutally killed in their Palmerston North home in 2000.

Mark Lundy was first convicted of their murders in 2002, and his first appeal attempt resulted in the court increasing his prison 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, as well as time of death.

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

The Lundy family.

He appealed this to the Court of Appeal in October last year.

Today the court rejected that appeal.