The council will now scrutinise the way in which teaching budgets are delegated on the basis of average salaries not actual expenditure. This method has been used in Scotland as an alternative to that south of the border where critics claim that funding of actual salaries encourages heads to hire young teachers on lower salaries.
George Rubienski, a teacher representative on Edinburgh's education committee, immediately expressed unease at "going down the English road".
But John Dobie, Edinburgh's acting director of education, said no decision had been taken. There was, however, likely to be greater control over switching expenditure from teaching to non-teaching activities.
Mr Rubienski said later he would be satisfied if changes were accompanied by ring-fencing of teacher salaries.
Mr Dobie reported that schools' devolved budgets were expected to break even in the 1997-98 financial year but "variances" had crept in, particularly in per capita spending on books and equipment. There was a Pounds 1 million overspend on repairs and maintenance, partly funded by schools switching money from other areas.
Stirling and Dundee are also looking at changes in how they allocate costs to schools. But Gordon Jeyes, Stirling's director of education, described the move as an "accounting technicality" and said the authority would continue to resource schools on the basis of recruiting the best teachers.
Sandy Weston, education resource manager with Dundee City Council, said budgets might be set using actual not average salary costs. But it was simply an attempt to streamline financial records, which required two sets of figures to be kept.
He stressed that any variation in school costs that resulted would be adjusted in the following financial year. "There will therefore, be no real incentive for schools to appoint someone lower down the salary scale to save money, " Mr Weston said.
Dumfries and Galloway this week became the latest authority to review its devolved management arrangements in schools, although the exercise will initially be confined to secondary schools. In its case, the move is driven by the Government's "best value" policy, introduced to replace compulsory competitive tendering.
Councils have to report to the Scottish Office by next March on how they are delivering value-for-money services efficiently. Ministers retain the option of putting council services out to commercial tender if they are not happy with the results.
Dumfries and Galloway agreed on Tuesday to set up a review group on secondary school devolved management chaired by James Leggat, headteacher of Annan Academy.
Caroline Taylor, the education department's business manager, said that the review group would consider whether schools could be given more room for manoeuvre in their expenditure.
Although more than 90 per cent of school-based spending is devolved, this does not include budgets for staff development, learning support and special needs, school lets or full control over repairs and maintenance.
Schools also face restrictions in the amounts of money that can be switched from teaching into non-teaching areas, and must work within a staffing formula.