The man found guilty of the hammer murders of Lin and Megan Russell and the attempted murder of Josie Russell has been refused a new appeal.
Michael Stone was originally convicted of the 1996 attacks in Chillenden, Kent in 1998 and then again at a retrial three years later.
He appealed on a second occasion but that was rejected in 2005.
Mrs Russell and her daughters were targeted as they walked along a country lane. Megan was six and Josie was nine.
Stone is serving three life sentences and has been told he must serve at least 25 years in jail.
The Criminal Cases Review Commission (CCRC) sent a 75-page document to Stone's lawyers setting out its reasons for the refusal to grant a new appeal in January 2009.
It then considered further representations made by his lawyers in the light of the document.
The CCRC said it looked at more than 50 individual points raised by Stone's lawyers in application and carried out a "substantial amount" of fresh forensic testing on material from the crime scene.
The CCRC added that after detailed and "painstaking" new investigations it had found nothing to justify a new appeal hearing.
On the day of the murders, Dr Shaun Russell was told that he had lost his whole family.
It was only when a policeman at the scene noticed Josie move that it was realised she survived the attack.
After the killings, Josie and Dr Russell returned to the Nantlle valley in Gwynedd, where the family had been living before the move to Kent.
Josie went to the local Welsh-medium primary school and learnt to speak again. She later studied art and design at Bangor's Coleg Menai.