We present a search for the rare decays B→h()νν̄, where h() stands for a light meson. A data sample of 535×106 BB̄ 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→K0νν̄ and B+→K+νν̄ decays are more stringent than the previous constraints, while the first searches for B0→K0νν̄, π0νν̄, ρ0νν̄, νν̄ and B+→K*+νν̄, ρ+νν̄ are reported. © 2007 The American Physical Society.