A family rights lobby group is offering a $25,000 reward for new information about who killed Chris and Cru Kahui.
The three-month-old twins died in Auckland's Starship Children's Hospital in June 2006 after being admitted five days earlier with brain injuries.
Their father Chris Kahui was charged with their murders but was found not guilty in May 2008 in the High Court at Auckland.
Lobby group Family First has posted the reward for information or evidence which leads to the conviction of anyone responsible for the twins' deaths.
The group's director, Bob McCoskrie, says somebody in the Kahui family knows what happened and who is responsible.
Mr McCoskrie says the reward will be paid only if a conviction is secured.
But Lorraine Smith, the lawyer for Chris Kahui, says she doubts anything will be achieved by the reward.
Ms Smith says the wall of silence among family members which Family First says it is hoping to break never existed.
She says family members spoke to police at length and have nothing new to say.
Ms Smith says she understands people's concern that no one has been brought to justice.