The explicit internal signal stochastic resonance (EISSR) that happened in the Willamowski-Rossler reaction model was investigated. The z-variable's output signal-to-noise ratio (SNR) as a function of the noise intensity shows non-monotonic behavior, indicating the occurrence of EISSR. It is first found that EISSR happened in the periodic-2 oscillations state. A worthy noting point is that the fundamental frequency of the intrinsic period signal of the system is shifted little with the change of noise intensity. EISSR is a cooperative effect of the intrinsic period signal and external noise or fluctuations. Our studies have shown that EISSR can lead to noise-resistance of the chemical oscillator. (c) 2005 Published by Elsevier Ltd.