The former head, who cannot be named for legal reasons, was dropped by his supply agency this May when they saw the allegation on his criminal record disclosure form.
He contacted West Midlands police to find out what information it had, and was astonished when told that he had been investigated for an alleged indecent assault on his step-daughter.
The teacher - who does not have a step-daughter - later received an apology from the now-retired chief constable Sir Edward Crew who explained that his details had been confused with those of another man who shared the same unusual surname and date of birth.
The teacher demanded compensation from the police for defamation and loss of earnings during the half-term he could not work, and this week accepted pound;2,500.
But he remains unhappy with the lack of support he received from his union, who told him he had no hope of winning reimbursement.
He said: "I do not think it is fair to name the union, because I cannot be named. But I have decided to resign my membership because of the way my case was handled."
Criminal for half a term, Friday magazine, 11