Double-murderer Mark Lundy has applied to the Privy Council in London for permission to appeal against his conviction.
Lundy is serving a life sentence for bludgeoning his wife Christine and young daughter Amber to death at the family's Palmerston North home in 2000.
In 2002, the Court of Appeal threw out his case and increased his minimum non-parole period to 20 years.
The Privy Council says although Lundy has no automatic right to appeal against that ruling, he has sought permission to do so.
A decision is due next year on whether the Privy Council will allow him to pursue the case.
Ultimately, the Privy Council's law lords have the power to quash Lundy's conviction, which could lead to a retrial.
Christine Lundy's brother Glenn Weggery told Radio New Zealand's Checkpoint programme on Wednesday he just wants Lundy to get on with the appeal process so the family can get it over with and forget him.