An Optimistic fair exchange (OFE) protocol is a good way for two parties to exchange their digital items in a fair way such that at the end of the protocol, both of them receive their items or none of them receives anything. In 2008, Huang et al. presented an efficient OFE protocol, but there is a security problem in their scheme. If the trusted third party (TTP) is dishonest and colludes with the verifier, the TTP can complete the transaction without getting signer's agreement. To solve this problem, we propose an OFE protocol in which there is a tracing algorithm to detect the party who completes the transaction. Furthermore, we obtain the accountability property introduced by Huang et al. in 2011, more efficiently and in the standard model while their protocol is in the random oracle model. We prove the security of our scheme under the chosen-key model and multi-user setting in the standard model.