In the decision Justice Wylie said costs should lie where they fell.
But Reekie then filed an application seeking costs worth $5762, made up of lawyer costs, travel costs and phone bills.
Justice Wylie today said the general principle was that the unsuccessful party should pay costs, but it was at the court's discretion.
``In accordance with settled principle, I am not persuaded that it is appropriate to make a general costs order in favour of Mr Reekie. ``There is nothing to depart from the general rule that a litigant in person is not normally entitled to costs,'' he said.
But he said it was appropriate allow Reekie a contribution towards counsel fees incurred by him for the preparation and filing of his original statement of claim.
Reekie was awarded $1000 in costs, to be paid to him by the Department of Corrections.
Reekie was sentenced to preventive detention in 2003 with a minimum non-parole period of 25 years after being convicted on 31 charges, including abduction and rape, for offences against four female victims, aged between 11 and 69.
David Dougherty was earlier wrongly jailed for the 1992 abduction and rape of the 11-year-old girl.
He was cleared by DNA evidence.