This means that extracting important decisions from the party is often a lengthy task and with an unpredictable outcome. This in turn means that on occasion everyone else in politics must hold their breath while the party reaches a verdict.
Yesterday, despite appeals for patience, the rest of the political world gave every appearance of being thoroughly exasperated with the party's decision-making processes. Thursday was one of the messiest of many messy days in the peace process.
In practical terms, the divisions within the party reflect a fundamental divide within the wider Protestant population. The party is technically in favour of the peace process and the Good Friday Agreement, yet many of its major figures are opposed.
This public wrangling contrasts with the approach of other parties such as Sinn Fein and the Rev Ian Paisley's Democratic Unionists, which keep their internal debates behind closed doors and present united fronts to the world.
Some weeks ago, Mr Trimble appealed in vain to party members not to air their differences in television studios. The fact is that the Presbyterian tradition of dissent means individuals in the party have a historically sanctioned conviction that they have a right and in fact a duty to speak out.
An example of this can be seen in the record of Mr Trimble's deputy, John Taylor MP. Originally a strong advocate of the Good Friday Agreement, he withdrew his support two months ago, and yesterday reiterated his opposition to it. His move meant that seven of the party's 10 MPs oppose the agreement, as does its most prominent peer, Lord Molyneaux of Killead, a former party leader. Luckily for Mr Trimble, however, the parliamentary party is just one of a number of organs among which power and influence is distributed.
His first port of call was to his assembly members, who are clearly divided on the present issue. Since they are regarded as one of party's most moderate sections, this split is regarded as fairly ominous.
Beyond the assembly members lies the party executive, a much larger body whose decisions are more difficult to call. And beyond that again is the Ulster Unionist Council, which formally makes party policy: its meetings are attended by up to 700 delegates. Anti-Trimble elements often threaten to call an emergency session of the council, but more recently there has been speculation that, if he gets the package through the assembly party, he might take the initiative and himself summon a meeting on a "back me or sack me" basis.
Mr Trimble's first hurdle, however, is the assembly party, whose members include a significant handful not disposed to tolerate any departure from "no guns, no government". For the moment this is the key battleground. If the proposed deal is endorsed, it will then move on to the other hurdles.Reuse content