Fairness is an important property of secure electronic commerce. Most of e-payment protocols guarantee fairness by using a Trusted Third Party (TTP) or semi-trusted third party. There are few protocols without a trusted third party. Based on concurrent signature, the authors propose two protocols suitable for digital products transaction, one for mobile payment and the other for the transaction which has higher security requirements by customers. The most prominent character of their schemes is that there is no traditional TTP, so the network congestion can be avoided. Furthermore, the protocols satisfy fairness and some other characteristics.