The second encounter involving the two leaders came as verbal sparring continued on the related issues of IRA arms decommissioning and the formation of a new executive which would include Sinn Fein ministers.
Mr Adams's position is that the Good Friday agreement allows Sinn Fein automatic entry into the executive, but Mr Trimble is pressing for prior movement on the decommissioning issue first. At yesterday's meeting Sinn Fein raised concerns about by Mr Trimble's suggestion that other political parties in Northern Ireland could press ahead without Sinn Fein if IRA disarmament did not take place.
The authorities yesterday announced a further relaxation of security measures, easing back on the use of the army in the light of reduced violence since last month's Omagh bombing. Up to 400 troops are to be shipped out of Northern Ireland while routine army patrolling will be ended in the south Londonderry area from the weekend. The police and army are also to review the disposition of Northern Ireland's numerous military bases.
Meanwhile, police in both Northern Ireland and the Republic yesterday continued to question twelve people about the Omagh bombing. Six were arrested on each side of the border on Monday in a combined operation aimed at breaking up the Real IRA which planted the bomb.
Ronnie Flanagan, the Chief Constable of the RUC, said the troop reductions were being made as a result of an ongoing review of the security situation in which he has been engaged with the army. He said he was pleased to announce that an "improving security situation" allowed police to operate increasingly widely with a reduced military presence.
Dr Mo Mowlam, the Northern Ireland Secretary, said: "It's a process of normalisation which was part of the Good Friday agreement."
Although the new moves were presented as being purely the result of security considerations, the authorities will be hoping that they will facilitate movement on arms de-commissioning by republicans.
Martin McGuinness of Sinn Fein yesterday welcomed the moves as "a positive step in the right direction". He went on to call for "the dismantling of the huge military installations dotted across the six counties".
The troops returning to Britain are the remaining elements of two full battalions which were drafted into Northern Ireland as reinforcements in advance of the Drumcree parade disorder in early July. Some of these have already returned to base, although they remain technically under the command of the army in Northern Ireland and can be returned immediately if needed.
The members of 39 Regiment (Royal Artillery) and the 1st Battalion the Highlanders will return to their bases in Britain over the next two weeks. Two weeks ago the police announced the ending of routine army patrols in Belfast.