Barnard was a member of the Civil Co-Operation Bureau, a special forces organisation aimed at eliminating anti-apartheid
activists across the world.
He was out on parole after serving three years for two other murders when he shot dead anthropologist Webster outside his home in Troyeville in 1989.
In June 1998, he was sentenced to two life terms and 63 years imprisonment on a range of charges, including the murders of Webster and Mark Francis and attempted murder of the late Dullah Omar, who became a cabinet minister.
Barnard was refused parole in February, despite the parole board and National Council for Correctional Services recommending him for parole.
Counsel for Barnard, Roelof du Plessis, argued no good reasons existed for Justice and Correctional Services Minister Michael Masutha not to follow these recommendations.
He said it was common cause Barnard had not obtained any scholastic, academic or technical qualifications during the past 17 years, but said it should be taken into account he had completed numerous rehabilitation programmes and courses, including a certificate in law studies.
He accused Masutha of attempting to manipulate the wording of the policies in place at the time and acting in bad faith.
Du Plessis said the fact the crimes were committed while Barnard was out on parole could not be used again and applied in a prejudicial manner.
Marumo Moerane, for the minister, argued Barnard had committed premeditated, cold-blooded murders and his criminal history and the timespan of crimes had led the trial court to conclude he was a danger to society.
He conceded victim dialogue was not possible as the surviving family members of Webster and Francis could not be traced.