Aaron James Holliday, 31, was behind bars in the Alexander Maconochie Centre awaiting trial for child sexual abuse committed against young boys in the ACT. He was later found guilty.

Prosecutors said Holliday had approached another inmate, and offered a reward for him to organise people outside prison to kidnap the witnesses, force them to record new statements and then kill them.

The inmate didn't go through with the plan and reported Holliday to authorities.

Police said they found documents outlining the plot and scripts for the witnesses to read when they raided Holliday's cell in July 2010.

In 2014, a jury found Holliday guilty of urging the inmate to get someone else to kidnap the witnesses, however his conviction was later overturned on appeal.

Justice Michael Wigney, sitting on the ACT Court of Appeal, found that a person could not be convicted of incitement to procure a crime when the main crime - in this case kidnapping - had not happened.

"The offence incited (procuring the commission of the principal offence) is subject to a limitation or qualification: the principal offence must be committed by the third person for the procurer to be liable for that offence," Justice Wigney said.

"Because [the fellow inmate] did not successfully procure anyone to kidnap, and nobody was kidnapped, not only did [the inmate] not commit an offence, but Mr Holliday also could not be convicted of inciting [the inmate]."

Canberra prosecutors were given permission in February to challenge that decision in the High Court.

The case revolved around whether Holliday could be convicted of incitement by encouraging the inmate to get a third person to carry out the kidnapping.

Prosecutors argued the offence of incitement to procure the kidnap was committed when Holliday approached the inmate.

But the court unanimously threw out the appeal in a decision handed down in Melbourne on Wednesday.

In throwing out the appeal, the majority of the High Court bench ruled Holliday could not be convicted of urging the inmate to carry out the offence, when no kidnapping was committed, under the criminal code.

The judges found he couldn't be convicted of incitement unless he had urged a separate offence be committed.

They said the reasons outlined in their decision showed there was no offence of incitement to procure in the criminal code, and if that was "a gap or omission", it should be fixed.

"If the legislature wishes incitement to procure to be a discrete offence under the criminal code (and, given the serious nature of the conduct, that is an available view), then that is a matter for the legislature to consider; and it is for the legislature, if appropriate, to expressly provide for that offence."

Holliday remains in jail on the child sex offences.