The inquiry into the murder of LVF leader Billy Wright is set to go ahead after a judgement in the High Court.
LVF leader Billy Wright was shot dead in the Maze Prison in 1997
The inquiry was initially set up under the Prisons Act after the loyalist was shot dead in the Maze in 1997.
NI Secretary Peter Hain later changed it to the Inquiries Act 2005, which Wright's father David objected to.
A court ruled last month Mr Hain had acted unlawfully, however David Wright has waived his right to seek an order quashing Mr Hain's decision.
His barrister said that it was for "pragmatic and personal" reasons.
Mr Justice Deeny said costs of £3.9m pounds had already been incurred and the quashing of the inquiry would cause uncertainty and considerable delay.
David Wright waived right to seek an order quashing inquiry decision
Wright, 37, was shot dead by three INLA prisoners in the Maze on 27 December 1997.
Former Northern Ireland Secretary Paul Murphy announced the public inquiry into Wright's killing in November 2004 following allegations of security force collusion in his murder.