The deficiencies of the first threshold Guillou-Quisquater signature scheme presented by Li-San Liu, Cheng-Kang Chu and Wen-Guey Tzeng are analysised at first, and then a new threshold Guillou-Quisquater signature scheme is presented. The new scheme is unforgeable and robust against any adaptive adversary if the base Guillou-Quisquater signature scheme is unforgeable under the chosen message attack and computing the discrete logarithm modulo a prime is hard. This scheme can also achieve optimal resilience. However, the new scheme does not need the assumption that N is the product of two safe primes. The basic signature scheme underlying the new scheme is exactly Guillou-Quisquater signature scheme, and the additional strong computation assumption introduced by the first threshold Guillou-Quisquater scheme is weaken.