It emerged yesterday that the party leader, David Trimble, and his deputy, John Taylor, found themselves isolated in a key meeting before last month's crucial fisheries vote in the Commons. The other seven of the party's nine MPs rejected Mr Trimble's advice to vote against the Government, and instead abstained.
The significance of this for both the Government and Labour is that in Mr Trimble's manoeuvrings with the Tories and Labour in the months running up to the next election, a serious question-mark hangs over his ability to deliver the votes of his colleagues.
Ulster Unionist party sources yesterday confirmed an Irish Times report of Mr Trimble's 7-2 defeat at the parliamentary party meeting, which took place less than an hour before the fisheries vote, in which the Government had a majority of 11.
They also confirmed the description of the meeting as acrimonious. One MP said yesterday: "I never remember an incident like this before."
At the moment the majority of the nine MPs appear to be against any idea of bringing down the Conservatives. They point out that concessions have already been extracted from the Government on issues which include the toughening of the terms for Sinn Fein's entry into talks, the beef crisis and fishing quotas.
The feeling is that further useful concessions may also be wrung from the Government in the coming months. An MP added that helping to bring down the Government so close to the end of its natural life would in any event be "a meaningless gimmick."
A number of sources say that Mr Trimble has never succeeded in winning the confidence of his parliamentary colleagues since his election as leader over a year ago.