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Customers are usually passive in an electronic commerce transaction. Based on a new two times concurrent signature, this article presents a fair electronic payment (E-payment) protocol. It can protect both of the participants' profits. Whatpsilas more, in this protocol customers have more initiative, and they can terminate the transaction before possible cheats (while they also should be responsible for the quit), so their security is enhanced. As there is no traditional trusted third party (TTP) in our scheme, network congestion and conspiracy problem can be avoided. Moreover, the protocol satisfies fairness and non-repudiation, and it can also be applied in the digital signature or product exchange process.