The author of a government commissioned report reviewing the Parades Commission has said it needs to be re-formed.
Portadown Lodge has been at the centre of the decade-long dispute
Sir George Quigley also criticised the NIO for appointing two Orangemen to the body which "should be reconstituted".
He said those directly involved in the parades dispute should not be on the decision-making body.
On Friday, the High Court ruled the appointments of David Burrows and fellow Orangeman Don McKay were unlawful.
It said the appointments did not ensure membership of the body represented both sides of the community.
Sir George told the BBC's Politics Show on Sunday: "My feeling is, and certainly this was the conclusion of my report, that one should not have on the body those who are involved in the parades issue itself.
"You don't get over the difficulty by saying they will not be involved in their own area.
"Because, so many of these dispute are inter-related - we have the whole problem of feeder parades.
"I think you simply have got to get people of independence, common-sense, able to analyse the case."
DUP MP Jeffrey Donaldson said he agreed with Sir George.
He said his party supported reform and a new approach and he called for a balanced membership.
There were now no members of the DUP on the commission, said Mr Donaldson.
Joe Duffy, a resident of the nationalist Garvaghy Road in Portadown, went to the High Court last week seeking to overturn the appointment of Mr Burrows and Mr MacKay.
Don MacKay (left) and David Burrows are prominent Orangemen
Both Mr Burrows and Mr MacKay were members of the Portadown Lodge of the Orange Order which has been at the centre of the decade-long dispute surrounding their Drumcree parade.
Mr MacKay resigned from the commission earlier this week after it emerged he had listed DUP MP David Simpson and SDLP assembly member Dolores Kelly as referees on his application form without asking their permission.
Secretary of State Peter Hain said he would take legal advice over the High Court judgement.
The Parades Commission was set up in by the government in 1997 to make decisions on whether controversial parades should be restricted.