We report a search for the rare decays B -> h(*) nu nubar, where h(*) stands for K+, Ks0, K*+, K*0, pi+, pi0, rho+, rho0 and phi. The results are obtained from a 711 fb-1 data sample that contains 772 million BB pairs collected at the Y(4S) resonance with the Belle detector at the KEKB e+e- collider. We search for signal candidates by fully reconstructing a hadronic decay of the accompanying B meson and requiring a single h(*) meson left on the signal side. No significant signal is observed and we set upper limits on the branching fractions at 90% confidence level. The measurements of B+ -> K*+ nu nubar, B+ -> pi+ nu nubar, B0 -> pi0 nu nubar and B0 -> rho^0 nu nubar provide the worlds currently most restrictive limits.
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