In a (t, n) threshold proxy signature scheme, which is a variant of the proxy signature scheme, the proxy signature key is shared among a group of n proxy signers delegated by the original signer. Any t or more proxy signers can cooperatively sign messages on behalf of the original signer. In 2000, Hwang et al. (Int J Inf 11 (2000) 1) proposed a secure nonrepudiable threshold proxy signature scheme with known signers. In this paper, we point out a cryptanalysis of their scheme. Furthermore, we improve the security of the threshold proxy signature scheme which remedies the weakness of Hwang et al.'s scheme.