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The KTeV E799 experiment has conducted a search for the rare decays KL2!0?0æ+æ- and KL2!0?0X02!?0?0æ+æ-, where the X0 is a possible new neutral boson that was reported by the HyperCP experiment with a mass of (214.3 ± 0.5) MeV/c2. We find no evidence for either decay. We obtain upper limits of Br(KL2!0?0X0 2!?0?0æ+æ-) 1.0 x 10sup-10/sup and Br(KsubL/sub2!?sup0/sup?sup0/supæsup+/supæsup-/sup) 9.2 x 10sup-11/sup at the 90% confidence level. This result rules out the pseudoscalar Xsup0/sup as an explanation of the HyperCP result under the scenario that the ds̄X