To simulate the functionalities of the real cash, one of the important requirements of electronic cash systems is the anonymity of users. Unconditional anonymity, however, is also very well suited to support criminals in blackmailing. Recently Kügler and Vogt  proposed a payment system based on the blind undeniable signature that protects the privacy of the users and defeats blackmailing with the assumption that the victim of a blackmailing can inform the Bank of a blackmailing before delivering the money and transfer the decryption key(i.e. the secret key of the victim) used in confirmation protocol without being detected by a blackmailer. But the assumption that the victim is always able to inform the bank of blackmailing is very impractical in such cases as kidnapping and special impersonation. In this paper, we propose two practical methods that gives the Bank the information about blackmailing and decryption key without any unpractical assumptions.