  We present a search for the rare decays B -> h(*) nu nubar, where h(*) stands
for a light meson. A data sample of 535 million BBbar pairs collected with the
Belle detector at the KEKB e+e- collider is used. Signal candidates are
required to have an accompanying B meson fully reconstructed in a hadronic mode
and signal-side particles consistent with a single h(*) meson. No significant
signal is observed and we set upper limits on the branching fractions at 90%
confidence level. The limits on B0 -> K*0 nu nubar and B+ -> K+ nu nubar decays
are more stringent than the previous constraints, while the first searches for
B0 -> K0 nu nubar, pi0 nu nubar, rho0 nu nubar, phi nu nubar and B+ -> K*+ nu
nubar, rho+ nu nubar are reported.
