John Major won the Unionists' support at a meeting with Mr Molyneaux last Thursday. The new arrangement was consolidated by telephone just before the critical vote.
The discussion between the two party leaders took place despite an assurance from 10 Downing Street last weekend that a meeting between Mr Major and and Mr Molyneaux was not scheduled or listed.
Ken Maginnis, MP for Fermanagh and South Tyrone, told BBC Radio Ulster's Inside Politics programme that the next 'weeks and months' would see the emergence of a better form of government for the province 'which repudiates the kind of activities' of the Social Democratic and Labour Party (SDLP), the Irish Government and the Labour Party.
He added: 'We would summarise the arrangement that was arrived at between . . . Jim Molyneaux and the Prime Minister as providing an opportunity for better and more effective government for the people of Northern Ireland within the UK.'
In a comment that appeared to presage the establishment of a select committee for Northern Ireland - one of the Unionists' longstanding demands - Mr Maginnis said: 'I believe that you will see in the coming weeks and months a better form of government for Northern Ireland, something that this country is crying out for and something which repudiates the activities of John Hume (the SDLP leader), Dick Spring (the Irish Foreign Minister) and Kevin McNamara (Labour spokesman on Northern Ireland).'
The Unionists may also achieve a change in the way legislation affecting Northern Ireland is conducted. At present, laws are made through Orders in Council, which MPs are unable to amend, and Unionists MPs are pressing for adoption of the procedure used in the rest of the United Kingdom. More powers for local government could also be on the agenda.
Both Conservative and Unionist sources have stressed the informality of the new relationship between the two parties.
Government business managers do not believe that they can count on the automatic support of the nine Ulster Unionist MPs in every division, with the party judging issues on merit. Ministers say contact between the party leaders will be private and will usually take place at the Commons. But Unionists believe that they have won a seat at Westminster's top table and are now guaranteed a favourable hearing in Whitehall.
The new arrangement seems certain to provoke tension between London and Dublin although ministers have reassured their Irish counterparts that no deal has been struck. Nor is an early resumption to the inter-party talks in Northern Ireland now expected.
Stressing the incremental nature of the new relationship, Mr Maginnis said yesterday: 'We are not going to see the Ulster Unionist Party coming out with a little package all wrapped up in blue ribbon, waving it around saying here is the short-term advantage we got for being lobby fodder.'
But he was adamant that the Unionists had achieved gains.
However, in an acrimonious confrontation with Mr Maginnis, Peter Robinson, deputy leader of the Democratic Unionists, said he was convinced the Ulster Unionists had emerged empty-handed from the bargaining.
For their troubles, though, the Ulster Unionists were now committed to supporting the Government throughout the life of this Parliament, said Mr Robinson, who, like his colleagues, voted with the Oppositiion.
'They have tied themselves to the apron strings of the man who goes down to Dublin and has meetings on the basis of the Anglo-Irish Agreement', he said.