Current e-cash systems enable anonymity services to protect users' privacy, but most of them do not provide the non-repudiation service such that many problems exist in the systems like denying, losing, misusing, stealing, and double-spending, etc. This paper proposes an e-cash system in which a one-time public key is embedded in the partial blind signature to provide the non-repudiation service against the above attacks. The article also demonstrates that the combination of the partial blind digital signature and anonymous digital signature makes the e-cash systems more robust and fair than before.