The false alarm probability of eavesdropping checks on both AliceBob quantum channel and AliceCharlie quantum channel in the controllable quantum secret sharing protocol using GreenbergerHorneZeilinger states proposed by Y. Sun et al. is analyzed. The reason why the total false alarm probability of eavesdropping checks in the controllable quantum secret sharing protocol using GreenbergerHorneZeilinger states is not equal to 0 lies in the randomness of measurement basis selection for eavesdropping checks. Afterward, an improved controllable quantum secret sharing protocol using GreenbergerHorneZeilinger states is proposed, based on using deterministic measurement basis for eavesdropping checks. Theoretical analysis shows that compared with the original one, the improved scheme can discover the eavesdropping from any internal dishonest participant with twice probability, and possesses much higher security. Moreover, the total false alarm probability of eavesdropping checks in the improved scheme is equal to 0.