Abstract: Fairness is one of the basic requirements of E commerce protocols CEMBS is proved to be an important cryptographic building primitive in constructing fair exchange protocols In this paper flaws of the existing CEMBS implementing methods are analyzed A new CEMBS constructing method based on RSA cryptosystem is proposed, which is proved to be simple, efficient and secure Afterwards, a fair exchange protocol is built using the newly constructed CEMBS And the devised scheme is the first efficient CEMBS based on RSA, which is the most popular public key cryptosystem