In this article, the question about how to describe the space correlation of the fluctuation in a chemical reaction system has been analysed. Eeferring to the reaction-diffusion equation., we have successfully introduced the diffusion or pressure terms into master equation of the probability distribution function of density. Solving this master equation for infinite medium, a series of waves have been obtained. The first branch is the average density wave which has already been obtained from the reaction-diffusion equation. It is just the acoustic wave in gases. Other branches decribe the propagation of the fluctuation moments of the local density. They present the propagation processes of the local distortion of the probability distribution function. The method to solve the initial problem of the master equation have also been discussed.