Edinburgh Council said it expects an independent inquiry into the closure of 17 schools in the city to conclude before the end of the year.
Chief executive Andrew Kerr is leading the search for someone to chair the inquiry and determine its remit.
He hopes to appoint an industry figure with experience of Private Finance building contracts by the summer.
The council said all schools are due to open in time for the new term in August when the inquiry will begin.
The schools were closed last month over safety fears when a wall collapsed at Oxgangs Primary School and others were found to be missing vital wall ties.
Children at all 17 schools are now back in classrooms but finding alternative accommodation was a major logistical operation and some youngsters face lengthy journeys to temporary sites.
Andrew Burns, City of Edinburgh council’s leader, said: “I’m pleased to be able to say that the progress is been quite rapid in recent days and we are still on schedule to have three of the schools reopening this month in May, five schools next month in June and the remaining nine schools by the middle of August for the start of the new term.”
Melanie Main, Edinburgh’s Green education spokeswoman, said: “This update report is woefully inadequate in the detail it provides.
“What is required is a full, in depth inquiry with a agreement on what the inquiry will cover.
“It is neither clear who will make these decisions nor what will be included in scope, but, if it turns out that the Labour/SNP administration intend to make these decisions behind closed doors, that would be unacceptable.
“If the confidence of the public and school communities is to be restored this fiasco must be carefully examined so that the facts can be laid out honestly and publicly and the right steps be taken to ensure the council can provide safe, fit for purpose schools for our children well into the future.”