Sef Gonzales received three life sentences in 2004 after being found guilty of murdering his solicitor father, Teddy, 46, his office manager mother, Mary, 43, and his 18-year-old high school student sister, Clodine.

They all sustained multiple stab wounds, while his sister also was hit with a bat, in their northwest Sydney home in July 2001.

An appeal against his convictions and sentences was dismissed in 2007, and applications for a special inquiry into the convictions were dismissed in 2018 and 2019.

In a NSW Supreme Court decision published on Friday, Justice Des Fagan found there no special facts or circumstances that would justify the taking of further action.

"The sole ground of the present application is that evidence adduced by the Crown from the applicant's aunt, Ms Emily Luna, gave rise to a reasonable doubt concerning his guilt, to which the jury should have given effect by acquitting him," the judge said.

She testified she had gone to the house at about 6.05pm on the night of the murders and rang the doorbell three times.

She said she waited about five minutes during which time she saw through the frosted glass panel on the left side of the door what she initially believed to be a coat stand with a hat and long jacket.

But after taking part in a reconstruction of what she had seen, she testified she came to the view that "it was actually a person standing there" who was standing completely still.

The Crown relied upon her evidence in support of an inference that the perpetrator was still in the house approximately 45 minutes after the mother was killed and before her husband arrived home at about 6.45pm.

Their son's inquiry application related to evidence given about the aunt's height, the shoes she was wearing and the height of her nephew.

"It was for the jury to determine whether the evidence 'establishes' that the person inside the house was taller than the applicant and was therefore someone else," Justice Fagan said.

"A doubt or question could only rise if the evidence of Ms Luna that is said to have been exculpatory was such that a reasonable jury, properly instructed, had to regard as giving rise to a reasonable doubt.

"The evidence was of negligible weight and significance.

"It was well open to the jury to put it one side as not giving rise to any reasonable doubt, having regard to an otherwise very strong Crown case."

The Crown had alleged Gonzales committed the murders because he wanted to inherit his parents' property.

Australian Associated Press