  We report on a search for a heavy neutrino in the decays $\tau^- \to \pi^-
\nu_h$, $\nu_h \to \pi^\pm \ell-+$, $\ell = e, \mu$. The results are obtained
using the full data sample collected with the Belle detector at the KEKB
asymmetric energy $e^+e^-$ collider. We observe no significant signal and set
90% CL upper limits on the couplings of the heavy right-handed neutrinos to the
conventional SM left-handed neutrinos in the mass range 0.2-1.6 GeV/c$^2$.
