Former Stormont Economy Minister Sir Reg Empey today hit out at suggestions that the deeply divided party could benefit from replacing its leader Mr David Trimble.
Mr Empey, who has been touted as a possible successor to Mr Trimble, insisted it was not the time for "musical chairs".
"People's names have been mentioned in the press last week. In fact, most people's names have probably been mentioned," the UUP vice president said.
"But the reality is if you look at what happened to the Conservative Party, they changed leaders and what difference did that make?
"Of course there are personality issues but playing musical chairs with a leader isn't a solution of itself.
"There are a whole cocktail of issues which have to be addressed and policy remains a major one of those. The personality stuff comes and goes."
Mr Empey, who abstained in yesterday's vote by party officers to discipline the three rebel MPs, said there needed to be some form of internal discussion to resolve the dispute.
The row within the UUP, he argued, was also distracting unionists from the real issues in the peace process.
"Two things happened this week that received very little attention," the east Belfast councillor told BBC Radio Ulster.
"Republicanism and its failure to honour its obligations under the Belfast Agreement hasn't been mentioned - that's the first thing.
"The second thing that happened this week was on Monday (DUP leader) Ian Paisley launched his new document `Towards a New Agreement'.
"Not only was the document vacuous and contained nothing of substance but he has added a huge dimension to the DUP's policy by saying he now requires the disbandment of Sinn Fein, as it currently stands, before there will be any negotiation with republicans."
PA