Noise-induced Ca2+ signal (NICS) was explored in Ca2+ system. But how far from the bifurcation point, could one get the admissible region of NICS? We proposed and demonstrated numerically that there existed a critical threshold of NICS, and discussed the relationships of the noise intensity, the distance to the bifurcation point, and the critical threshold. Furthermore, the detailed bifurcation diagram for certain noise intensity was renewed. Finally, it was found that not all the NICS but partial NICS was optimized selectively with the assistance of noise. (c) 2006 Elsevier B.V. All rights reserved.