A deniable authentication can be used to provide secure negotiation on the Internet. Although many deniable authentication protocols have been proposed, most of them are interactive or vulnerable to various cryptanalytic attacks. To find a secure and efficient deniable authentication protocol, by encrypting a random and the time stamp and signing the corresponding ciphertext and the message to be sent with Schnorr signature scheme, a new deniable authentication protocol is proposed. The non-interactive manners make that the new scheme is efficient. On the other hand, the new deniable protocol not only has the properties deniability and completeness but also has the enhanced security. The proposed scheme can be proved to be secure against forgery attack, impersonation attack, compromised session secret attack and key compromise impersonation (KCI) attack.