The Dominican order, which has 24 schools North and South, has started a process of transferring legal and financial responsibility for them to local dioceses and others, because of a sharp drop in its numbers.
The order plans to transfer legal and financial responsibility for its nine primary schools to dioceses situated all over Ireland, and is working on a new structure for its 13 second level schools, including Sion Hill and Muckross in Dublin.
However it said the ethos and vision of the schools would be maintained and their day-to-day operations would be unaffected.
Several prominent public figures have attended Dominican schools, among them the President, Mrs McAleese, and broadcaster Marian Finucane.
The order has spent the last six weeks briefing its staff at 17 regional seminars and it has produced a new document entitled In Search of Truth: The Dominican Way in Education, outlining a new way forward.
The move is part of an ongoing change in education, with religious orders redefining their role and the laity taking on increased responsibility.
Sister Brid Roe, education co-ordinator of the order, said the process had been ongoing for some time, but it was impossible to say when it would conclude. "We are working our way through the process."
The order is also trustee to two teacher training colleges - St Catherine's (which trains primary teachers) and Froebel College in Blackrock, Co Dublin - which will also be transferred to some other body or structure.
The order said it had arrived at the decision reluctantly, but it was important that new structures were set up to guard the future of the schools, particularly their ethos and vision. The boards of management of the schools have been informed.
For parents and children in the schools there should be no noticeable change, as many already have lay principals and the number of nuns teaching now is very small.
Several large orders and congregations - including the Sisters of Mercy, the Christian Brothers and the Holy Ghost Fathers - have also spoken about their plans to scale down their involvement in the running of schools.
The Dominican Order has some of the most prominent schools in the education sector, with Muckross College and Sion Hill in Dublin and Wicklow Dominican College particularly well known.
Several of the primary schools have already been transferred, including three in the Ballyfermot area and one in Belfast, St Catherine's on the Falls Road. Sister Roe said the Dominicans were currently working on a new model for the second level schools. She said this would either be a regional trust made up of several orders or a single trust, also made up of several orders.
The order's decision to transfer St Catherine's to the local diocese of Down and Connor has caused some parents distress. One parent, Mr Daniel Bartsch, has written to the order asking it to reverse its decision. He claims the site of a new school for St Catherine's in Lanark Way is near a peace line and is very dangerous. St Catherine's will be merged with two other Catholic schools at this location.