It's the only state-funded single-sex school in Scotland - and it's in the West End of Glasgow.
Now parents are applying fresh pressure to open up Notre Dame High School to boys - as well as girls who currently attend.
They have gathered cross-party support for a consultation to explore the options and gauge desire for change.
A petition has also been launched to apply pressure on the city's education authority.
The situation is complex and opinion split.
Many families across the wider city value the choice to send their daughters to a state-funded all-girls school.
But local families say that discriminates against their wish to have their children attend a school near to where they live.
Labour, the Greens and Conservatives say there is a need for a consultation.
Parents have called their campaign Notre Dame High For All (NDH4ALL).
Campaign spokesperson Niamh Breakey is a mum of three boys at Notre Dame Primary School.
She says: “The current situation is blatantly unfair as our children are the only primary school pupils in Scotland that do not have the right to transition to their local secondary with their siblings and friends.
"Notre Dame High is a local secondary school, but it is excluding and failing local children with this antiquated policy.”
Boys and girls at Notre Dame Primary School are educated successfully together through to Primary 7, say parents.
The issue for local parents is that boys then have no right to attend any of the four local secondary schools.
They are only guaranteed a place two miles away at St Thomas Aquinas Secondary.
Girls can attend the local Notre Dame High but have no right to attend any co-educational school which is the preferred choice of most parents at the primary.
Pupils end up scattered across up to a dozen schools in the area, despite Notre Dame High School operating significantly under its capacity, say parents.
Niamh says: “Rather than send children out of their community, families often rely on placing requests to local non-denominational schools, but there’s no guarantee they’ll be accepted due to pressure on places.
"Meanwhile the High School is not even full, as many parents of girls do not want single-sex education.”
She adds: “Cllr Cunningham, the Education Convenor, and his SNP colleagues were elected on a manifesto of promoting ‘an inclusive, non-discriminatory learning environment’ and ‘giving every child and young person an equal chance to fulfil their potential’.
"How is it inclusive, non-discriminatory or fair, to be funding a local high school that denies access to local children, just because of their gender?”
Jane Kennedy, mother of three girls including two at primary school, says there is a need for change.
She says: “My eldest daughter’s closest friends are boys.
"I am really concerned that she will be prevented from maintaining those friendships as she goes through the often stressful transition to secondary school.”
Mr Cris Biguzzi, father of a boy and girl at primary school, said: “It’s important to me that my children can walk to school, and participate in after-school activities.
"There is a strong sense of community at Notre Dame Primary with parents very actively supporting the school.
"All of that becomes very difficult if they attend school miles away from home; or we have to travel to two schools for everything because our son isn’t allowed to attend the same school as his sister.”
Glasgow City Council rejected a request for a consultation in November 2017.
NDH4ALL says at the time the council justified its decision partly on the basis that Notre Dame High School is a high-attaining school.
'DIVERSITY OF OPINION'
But parents say that results at Notre Dame High are no better than other co-educational schools in the area - even when pupils’ backgrounds are taken into account.
Mrs Breakey added: “There are a small number of parents who want to keep the status quo where, for example in S1 72 per cent of girls travel from outside the local area to the high school.
"Those parents already have the right to educate their girls locally and are effectively arguing that they should retain a second option to choose single-sex education for their daughters.
"In the meantime, our boys have neither option solely because of their gender.”
Councillor Martin Rhodes, the local Labour councillor said: "I understand that this is an issue which could affect thousands of people across our city, and that there is a diversity of opinion amongst parents and carers.
"As such, we are of the view that any decision should be informed by as wide a range of input as possible.”
Councillor Tanya Wisely of the Greens added: “The Green Councillor Group is fully supportive of the NDH4All parents group’s call for a consultation on gender segregation at Notre Dame High, the only single-sex state school in Scotland."
The Scottish Conservatives have also stated their support for the parents' call for a consultation.
The city is currently consulting on a city-wide review of the catchment system - which they say has to take precedence over the situation in the West End.
A council spokeswoman said: “Our secondary school catchment consultation will result in a consistent system being adopted across Glasgow and has to be concluded before we can consider a consultation on the future of Notre Dame High School
“Education officers continue to liaise with the various parent groups who have a range of opinions.
“We would urge all interested parties to make their views known as part of the secondary catchment exercise in order that they shape any future potential changes.”