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Based on new understanding of proxy signature, we propose a new threshold proxy signature scheme. Compared with previously proposed schemes it has some new properties. It uses a warrant, which is agreed and signed by the original signer and all proxy signers together. It has no independent proxy shares stage, which is finished in proxy warrant agreement and signature stage. Its computation complexity and communication cost have nothing to do with the size of the proxy group. Moreover, in the new scheme the verification of proxy signature is divided into two steps, one is the verification of the warrant, the other is the verification of the proxy signature. Having these properties, the proposed threshold proxy signature scheme has less computation and communication cost, compared with previously proposed schemes based on discrete logarithms, it withstands the warrant attack and signature forgery attack. It is more efficient and secure.