The decision to acquit prominent loyalist William "Mo" Courtney is to be taken to the Court of Appeal.
Willliam "Mo" Courtney was acquitted of murder
He was freed from Belfast Crown Court on Thursday after the judge upheld his acquittal over the killing of Alan "Bucky" McCullough.
Prosecuting QC Geoffrey Millar said they would appeal on the grounds an error was made in deciding the 43-year-old had no case to answer.
Mr Courtney, of Fernhill Heights, was tried under the Diplock no-jury system.
On Tuesday Belfast Crown Court judge Mr Justice McLaughlin said he could not convict him of the 2003 murder of Alan McCullough - a former associate of UDA leader Johnny Adair - or UFF and UDA membership.
As Mr Courtney was freed on his own bail of £100 on Thursday, the judge said he had been thrust into a difficult position after ruling that the evidence was not strong enough to convict him.
"I have made it clear that the ruling I gave two days ago was not intended to be a detailed analysis of all the evidence," he said.
"It purports to be nothing more than an analysis of certain portions of evidence which, in my opinion, left such gaps in the prosecution case that I had to come to the conclusion there were no circumstances in which I could properly convict.
"The prosecution now invites me to allow them to appeal that conclusion.
The body of Alan McCullough was found in a shallow grave
"It seems to me there's something of a conflict between me having reached that decision and now saying there is no arguable case to grant leave.
"I'm not very happy that the prosecution has established the basis upon which it should be given leave (to appeal)."
As he refused the application, Mr Justice McLaughlin accepted that the prosecution was free to put its case before the three Appeal Court judges.
He added that he had proceeded with caution because it was the first time a judge sitting in a Diplock trial in Northern Ireland had been put in such a position.
The body of Mr McCullough, 21, was found in a shallow grave on the outskirts of north Belfast. He had been shot.
An earlier hearing had been told that Mr McCullough had been a member of the so-called "C company" of the UDA - headed by Adair.
"C company" had been expelled from the UDA in 2002, and a number of its members, including the victim, had been ordered out of Northern Ireland by UDA leaders.
Mr McCullough returned to Northern Ireland in April 2003 and his body was found on 5 June.