Based on a digital signature with message recovery, we present a new fair non-repudiation protocol with features of security, efficiency and economical use of net resources. It has the properties of fairness，non-repudiation，secrecy，termination， etc。The third party of the protocol intervenes into the exchange in case of problems，and it need not be completely trusted，because the message which is exchanged between the parties is secret to the third party。In addition， its fault can be identified。So the protocol can optimize exchanges via Internet。