The North's First Minister, Mr David Trimble, has described the manner in which the IRA is returning nine bodies of the disappeared to their families as "dreadful".
The Ulster Unionist leader, however, said the return of the bodies would ease the years of anguish felt by the families.
"I'm glad obviously for the relatives of the disappeared that bodies are being recovered and, of course, their position is the priority in this.
"It's such a shame, though, that it's taken so long for this to happen, and for it to be done in such a dreadful hole-in-the-corner way is a bit sad," he said.
According to Mr Trimble, the manner in which the bodies were being revealed "detracted considerably" from the event. "But at the same time you realise the extent of the anguish that families have suffered over the years and that is now at least coming to an end," he added.
Comments made by the Sinn Fein president, Mr Gerry Adams, last Friday, that the return of the bodies to the families was a "human rights issue" and "a justice issue" were criticised yesterday by the Alliance Party.
Dr Philip McGarry, the Alliance president, said the remarks by Mr Adams were a shameful insult to the families of the victims. He said the comments showed that Sinn Fein inhabited a fantasy world where republicans could do no wrong.
"The disappeared were inexcusably murdered by the IRA. A conscious decision was made by republicans to torture the families of their victims by hiding the bodies, an act of unique barbarity. Republicans lied over the years about the graves and have only moved now because of public pressure.
"For Gerry Adams to claim a human rights motivation for Sinn Fein adds insult to the injury of the families. The fact is that Gerry Adams and his associates have come to believe all their self-serving propaganda, and they inhabit a fantasy world in which republicans, no matter how black their deeds, are always the victims whose human rights are being abused," Dr McGarry added.
However, the Sinn Fein chairman, Mr Mitchel McLaughlin, has stressed that the decision by the IRA to locate the bodies represents a wider message from the republican movement. "It is an outstanding issue of human rights and justice that could and should be resolved in the context of resolving other outstanding issues," he said.
The Bishop of Down and Connor, Dr Patrick Walsh, welcomed the efforts to recover the remains.