The Convention of Scottish Local Authorities and Unison have backed demands from the Association of Local Authority Chief Executives for Scottish procedures in line with those in England.
Mark Irvine, head of local government at Unison Scotland, said there had been too many cases of council chiefs being forced from their jobs without any explanation as to the circumstances involved.
COSLA chief executive Douglas Sinclair said the convention had already accepted the need for a review after Tony Connell, chief executive of Moray Council, left his job last year following allegations of expenses irregularities.
Mr Reiter took extended leave in October, just five months after his appointment, following allegations he had misled members about his involvement in the Westminster homes for votes scandal.
He never returned to his desk, even though an independent adviser had told the council there was no evidence of misconduct. Mr Reiter had also been cleared of any blame in the gerrymandering scandal by Westminster district auditor John Magill.
Unlike in England and Wales, councillors in Scotland are not obliged to accept recommendations from an independent adviser but must simply consider them.
Shetland convenor Lewis Smith, who is a vice-president of COSLA, said he hoped to be part of the COSLA/trade union body reviewing procedures.He argued that 'they haven't got it right in England either'.
'As well as chief executives needing protection, so do councils,' he said. 'An efficient voluntary system is also probably better than a statutory one.'
Shetland said: 'The council and their chief executive, Nick Reiter, have decided it is in the best interests of local government in Shetland for there to be a parting of the ways on agreed terms.'
Mr Reiter, who had the previous day told LGC of his desire to return to his desk (LGC, 8 January), said: 'I am sorry to be leaving Shetland, but I have taken time to consider my position with the council and have decided it is time to move on.'