We report the results of a high-statistics search for H dibaryon production in inclusive Υ(1S) and Υ(2S) decays. No indication of an H dibaryon with a mass near the M(H)=2m(Λ) threshold is seen in either the H→Λpπ(-) or ΛΛ decay channels and 90% confidence level branching-fraction upper limits are set that are between one and two orders of magnitude below the measured branching fractions for inclusive Υ(1S) and Υ(2S) decays to antideuterons. Since Υ(1S,2S) decays produce flavor-SU(3)-symmetric final states, these results put stringent constraints on H dibaryon properties. The results are based on analyses of 102 million Υ(1S) and 158 million Υ(2S) events collected with the Belle detector at the KEKB e(+)e(-) collider.