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The translocation dynamics of a single biopolymer chain through a nanopore in a membrane is investigated by taking the coil-helix transition into account. Based on the changing of the free energy due to the coil-helix transition, the mean first passage time τ is obtained, and then the corresponding numerical simulations are presented under different conditions. It is shown that the coil helix transition can significantly shorten the translocation time of the biopolymer chain. In addition, we also discuss the scaling behaviour for τ with the chain length N and some related problems.