Many applications of E-business need to solve the following problems of privacy and fairness for counter parties: without loss of generality for two traders, how to assure their clandestine trade with satisfying both sides, or protect rights when either of traders has a dispute? In this paper we develop a novel scheme, called FKESS, to settle the aforementioned typical problem. Its main idea is to judiciously choose a proof (called a keystone) during both sides agree on a session key. We give a full specification of this scheme, including how to realize specific properties by analyzing cryptography tools, how to define the complete fairness and design the scheme, and how to prove the scheme based on random oracle model. A primary advantage of the scheme is that it can be adopted among any traders in private without the trusted third party involved, but when the keystone will be published any one can become the arbiter. We contrast with typical related literature to evaluate the scheme, and show the significant performance improvements on the existing scheme.