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We present a new search for H0V production, where H0 is a scalar Higgs boson decaying into b b̅ with branching ratio β, and V is a Z0 boson decaying into e+e-, µ+µ-, or νν̅. This search is then combined with previous searches for H0V where V is a W± boson or a hadronically decaying Z0. The data sample consists of 106±4 pb-1 of p p̅ collisions at √s=1.8 TeV accumulated by the Collider Detector at Fermilab. Observing no evidence of a signal, we set 95% Bayesian credibility level upper limits on σ (p p̅→H0V)× β. For H0 masses of 90, 110, and 130 GeV/c2, the limits are 7.8, 7.2, and 6.6 pb, respectively.