A county council spent £32,000 on trying to recruit a new chief executive - only to find no-one suitable for the £170,000 a year role.
The Conservative-run Suffolk County Council interviewed candidates to replace Deborah Cadman on Monday following a "thorough search".
But no-one met "the exceptionally high standards" the council had, so a new search will begin.
The leader of the opposing Labour Party called it a "lost opportunity".
Ms Cadman is leaving the role to take up the same position at the newly-formed West Midlands Combined Authority.
Four men were shortlisted for the job and had a day of interviews and assessments.
Council leader Colin Noble said that while the lack of a replacement was "disappointing", the authority needed "to make the right decision for Suffolk".
"We face some extremely challenging times ahead, and must have the strongest possible chief executive to help us deliver change at the scale and pace we need, but also in a way that is appropriate for our county," he said.
"If that takes a little more time and searching, then we believe that's the right thing to do."
Corporate director Sue Cook is currently acting as interim chief executive and will continue in the role.
Councillor Sandra Gage, Labour, said: "A second attempt in the coming months offers no guarantee of a different outcome, and leaves Suffolk County Council months of having to 'make do' with the corporate management team filling the gap.
"A second recruitment is unlikely to happen until spring next year, and further costs will be incurred through likely extension of the interim staffing, temporary appointments of staff to take the council through the critical budget setting months of November through to February.
"Last night's decision leaves Suffolk County Council in an unnecessarily vulnerable position."