A non-repudiation protocol is aimed for exchanging a digital message and an irrefutable receipt between two mistrusting parties over the Internet. Such a protocol is said fair, if at the end of any possible protocol execution, either both parties obtain their expected items or neither party does. In this paper, we first argue that it is really meaningful in practice to exploit generic fair non-repudiation protocols with transparent off-line TTP. Namely, in those protocols, each involved party could use any secure digital signature algorithm to produce non-repudiation evidences; and the issued evidences are the same regardless of whether the TTP is involved or not. Then, we present such a fair non-repudiation protocol to overcome the limitations and shortcomings in previous schemes. Technical discussions are provided to show that our protocol is both secure and very efficient. In addition, some extensions are also pointed out.