The H-dibaryon resonance was sought by a ΛΛ invariant mass spectrum that was obtained by the C12 (K-,K+ΛΛX) reactions. We observed a bump near the ΛΛ threshold, as reported by the previous experiment (KEK E224), with better statistics. Data were compared with results of a cascade model calculation including ΛΛ final state interactions consistent with the newly measured binding energy of ΛΛ6He. No significant enhancements above levels of the model predictions were observed. The resulting upper limit for the production cross section of the H with a mass range between the ΛΛ and ΞN threshold is found to be 2.1 ± 0.6 (stat.) ± 0.1 (syst.) μb/sr at a 90% confidence level.