Key authentication is very important in secret communications and data security. Lee et al. proposed a new public key authentication scheme for cryptosystems based on discrete logarithms in 2003. Recently, Zhang et al. pointed out that Lee et al.'s scheme was not secure and proposed an improvement on it. However, in this paper, we will demonstrate that a dishonest user can forge the public key via the verification equation in the improved scheme. Therefore, Zhang et al.'s scheme does not achieve non-repudiation of the user's public key.