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The current quark mass model is adopted to study the phase transition of two-flavor quark matter to more stable three-flavor quark matter in the whole core of a supernova. It shows that the timescale of the process is shorter than 10-8 seconds, thatthe u- and d-quark masses can be neglected completely in this model, and that the temperature and the total neutrino energies in the core after the conversion increase nearly by 40% and 20% on the average compared with former results, respectively. The last result can further enhance the probability of success for a supernova explosion significantly.