We propose a new method to search for a sterile neutrino that mixes predominantly with a τ-neutrino and is lighter than the τ-lepton. The method uses the large e⁺e^- → τ⁺τ^- samples collected at B-factory experiments to produce the sterile neutrino in τ-lepton decays.  The sensitivity of the method is up to 10 times tighter than the current limit when using current B-factory data, and by 2 orders of magnitude with the full Belle II data sample. In addition, this method enables measurement of the sterile neutrino mass despite the presence of an undetectable neutrino.