Abstract A (t, n) threshold proxy signature scheme allows any t or more proxy signers to cooperatively sign messages on behalf of an original signer, but t−1 or fewer proxy signers cannot. Sun et al. proposed a new (t, n) threshold proxy signature scheme based on Zhang's threshold proxy signature scheme. Recently, Hsu et al. pointed out that Sun's scheme suffered from a drawback and proposed an improvement to counter it. However, the author of this paper shows that both Sun's scheme and Hsu's improvement are not secure against coalition attack. Some t or more malicious proxy signers can conspire together against the original signer. Finally, we propose a new improvement to counter this attack, the proxy generation and the signature computation of which is more efficient than those of Sun's scheme and Hsu's improvement. The main advantage of the new improvement is traceability, by which the original signer can identify the actual signers that are anonymous to outsiders.