The move is seen as significantly reducing the prospects for the type of widespread disturbances which have been seen in the last four years, beginning at Drumcree and spreading to many parts of Northern Ireland.
Everyone is nonetheless aware that the problem retains the potential to flare up again. While the Orange Order refuses to meet Catholic residents of the disputed Garvaghy Road area, Ulster Unionist leader David Trimble is involved in meetings with local nationalists. The holy grail for Mr Trimble and most other political elements would be the emergence of a formula which would manage to resolve the Drumcree issue and the wider arms de-commissioning disagreement.
While such a panacea remains elusive, the search for it will continue at Downing Street today when Tony Blair and the Irish Taoiseach, Bertie Ahern, resume talks with the Ulster Unionists, Sinn Fein and others. While no one is predicting an immediate breakthrough, some observers claim they scent that some progress is being made.
It became clear yesterday that more internecine unionist strife is on the way when Robert McCartney, leader of the United Kingdom Unionist party, announced that he will run in the European elections. Although Mr McCartney's party is small he is a prominent and combative figure whose candidature will ensure a lively campaign. He and Mr Trimble's party exchanged angry broadsides yesterday.
The Rev Ian Paisley, who has invariably topped the polls in the European election, will be seeking to do so again, and in the process to undermine the Good Friday agreement.
The fourth Unionist candidate is David Ervine of the Progressive Unionist Party, a grouping which has paramilitary links and which supports the Good Friday accord. He said yesterday: "We are a young party filled with young people. We have the whole future ahead of us - hopefully, a rosey future for everyone in Northern Ireland." On Drumcree, contacts are to continue between Mr Trimble and local Catholic residents, who until recently complained that he had never met them. Yesterday three of the largest sections of the Orange Order said they had dropped plans to amass up to 100,000 members at Drumcree, a move which would have had grave security implications.
The Order is plainly troubled about the Drumcree issue. While just about every Orangeman believes it is important for their Portadown members to be able to stage a march which they believe is part of their heritage, many are also apprehensive about the prospect of violence.
Last year's prolonged stand-off, which led to many clashes and eventually to deaths, is generally seen as having damaged the Order's image and set back its cause. It is also seen as showing that, while the Order can bring thousands of protesters on to the streets, it then has no effective means of controlling them.