Blackford Brae school can accommodate up to 24 pupils with emotional or behavioural problems while a support team works with other children around the city threatened with exclusion to keep them in their own schools. But the service costs up to 30,000 per pupil.
One member of staff said: "People are concerned for some of these children, who are among the most difficult in Scotland."
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Hide AdMartin Crew, Barnardo's director for Scotland, said: "No conclusion over the future of the school has been reached yet."