Teachers at two schools which close in June, Crookston Castle and Woodside, have first choice of unpromoted vacancies. But most denominational schools are stipulating that posts must be filled by a Roman Catholic. All nine vacancies at St Mungo's Academy are restricted and four out of five at Bellarmine Secondary.
Barry Carmichael, Educational Institute of Scotland representative at Crookston Castle, said that teachers, including some Catholics, were "outraged". "This is essentially a human rights issue, and we asked the union to deal with it as a matter of urgency," Mr Carmichael said.
Willie Hart, Glasgow EIS secretary, said that after a joint consultative committee meeting on Monday the city had agreed to try to have some of the posts redefined. But the closing date for applications from Crookston Castle and Woodside is today (Friday).
Mr Carmichael said: "Why wait until fewer posts are available and teachers are faced with a more restricted choice?" Teachers claim that the affair violates an agreement with the former Strathclyde Region that the only unpromoted post for which an applicant would need approval by the Catholic Church would be in religious education.
They believe heads want to give themselves greater freedom in appointments.
John Oates, national field officer for the Catholic Education Commission, said the legal position was simple: "All posts require Church approval. Things start getting confused when some authorities enter into local agreements which depart from the law."
Glasgow education department had no one available to comment.