Northamptonshire CC last week ended talks with contractor Hyder Business Services, which would have taken over all its back office activities, despite having spent £1.2m on the project.
But a third partner, Milton Keynes Council, insisted it could strike a deal with Hyder.
The project, valued by Unison at £766m, would have seen staff from personnel, finance, information technology and general administration transferred to Hyder.
'The senior management team and other parts of the council have been reinforced and are now very much stronger. The council's financial position is better and it has much greater capacity to initiate change itself.'
Milton Keynes leader Isobel Wilson (Lib Dem) said its deal was unaffected by Northamptonshire's defection.
'We have tested this partnership at every opportunity - we are still on track for a deal with HBS,' she said. 'The position in Northamptonshire has always been more finely balanced. We continue to be in a position of strength, with both ourselves and HBS committed to securing a robust partnership.'
Unison welcomed the collapse of the Northamptonshire deal and continues to campaign against Milton Keynes' plan.