The future of the only state school in Scotland where all the pupils are girls is to be discussed.
Glasgow City Council has said it will hold a consultation on whether Notre Dame High School should start taking in boys.
Some parents in the west end of Glasgow want their sons to go to Notre Dame.
But any proposal is likely to meet fierce resistance from supporters of the school, which has only taught girls since its inception in 1897.
The consultation will start at some point after an ongoing review of school catchment areas across the city has been completed.
Notre Dame High, in Glasgow's Hyndland, is a Roman Catholic school but a number of girls from Muslim families also attend.
Some 70% of the children come from parts of the city outside the school's own catchment area.
A legal challenge to Notre Dame's status failed 16 years ago.
However, the parents of some children at one of the feeder primary schools want boys to be able to attend.
They have formed NDH4All Parents Group to express their views on the issue.
In a statement it said: "While we welcome Councillor Cunningham's announcement today that there will be a consultation on ending gender discrimination at Notre Dame High School, we are disappointed that no timescale has been given.
"It is highly unfair to have this uncertainty over our children's - and, indeed, the school's - future. Time is running out for our local children as they reach secondary age.
"Additionally, it is a huge waste of public time and money to review the entire city's secondary catchment areas and then later pick it apart again for one school. Notre Dame High School's gender entry requirements have to be addressed concurrently."
Some of them argue that their boys should be able to enrol at Notre Dame as the other secondary schools in the area are further away or less convenient.
Some also want their sons and daughters to be able to go to the same secondary school.
When Notre Dame opened 120 years ago, same sex education was not uncommon but other girls' schools in Scotland gradually closed or started admitting boys.
Parents of children who are currently at the school, and some former pupils, are likely to fight hard to maintain its unique status.
They are expected to highlight the fact that many parents actively choose to send their daughters there as being evidence there is a significant demand for an all-girls' school.
Speaking on the BBC's Good Morning Scotland programme, Co-chair of the Notre Dame High School Parent Council Michelle Watt said: "Parents whose children are at the high school and parents of children at the other feeder school in St Ninian's, who voted against any consultation, are very surprised by the timing of this.
"The school is performing exceptionally well.
"It has been in the community for over 100 years and has served the communities right across Glasgow for that length of time."
Although Notre Dame is the last state secondary in Scotland where all the pupils are girls, there are a number of similar schools south of the border.
Some - like Mulberry School in Tower Hamlets - enjoy excellent reputations and have attracted prestigious visitors including Michelle Obama.
However, sceptics would argue that schools like Notre Dame and Mulberry are successful because of the quality of the teaching and their ethos rather than because there are no male pupils.