A non-repudiation protocol enables the fair exchange of an electronic message and an irrefutable digital receipt between two mistrusting parties over the Internet. That is, at the end of any execution instance of such a protocol, 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 trusted third party (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 some limitations and shortcomings in previous schemes. Technical discussions are provided to show that our protocol is not only secure but also the most efficient solution, compared with existing non-repudiation protocols. In addition, some potential extensions are also pointed out.