The 14-pupil Quarff primary will share a headteacher with Cunningsburgh next door, while the depute head at Aith Junior High will look after the headship at Sandness, which has just eight pupils.

The move has been criticised by the local branch of the Educational Institute of Scotland which fears a hidden agenda to introduce “shared headships” by the back door.

Similar moves have been adopted in South Ayrshire, Scottish Borders and Highland as a way of keeping small schools open and freeing heads from the demands of teaching.

Shetland caused an uproar last year when it proposed closing five primary and two secondary schools, using shared headships as part of a best value review of the education service.

The public’s resentment was powerfully expressed during May’s local elections which saw the ruling Liberal Democrats evicted from office, with education the main issue at the ballot box.

This summer parents at Quarff and Sandness, two of the schools on the council’s hit list, were thrown into a panic after both headteachers announced they were to leave, one for another job and the other to retire.

Principal teachers will be appointed at Sandness and Quarff, but the schools will be administered from Aith and Cunningsburgh.

Bill Manson, the council’s education spokesman, said: “For good or ill, we have got a situation where the opportunities have occurred to try out two pilot schemes, with the approval of the parent bodies.

“This means that by the end of the best value review we will have had the experience of two joint school management schemes within this authority which will be very useful to both teaching and parental bodies.”

But Jean Marwick, local EIS secretary, voiced the union’s deep concerns.

“Last year parents and teachers gave a full-scale rejection to the idea of shared headships when they were proposed as a way forward for education by the council,” she said.

“Now the situation is slightly different, but we are seeing something very similar being brought in as it were by the back door. It has come up suddenly without much consultation, and certainly the unions have not been spoken to. This has set the alarm bells off and we want to make sure that this is very closely monitored and will not be seen as a route towards shared headships.”

Mr Manson said that during meetings with parents and the schools involved there had been a growing feeling of support.

Councillors agreed that if the pilot projects were a success, they should lead to three-year contracts for shared headships.