In this article, the wave solutions of multivariate master equation for linear reaction system: A→X have been discussed. Except the density waves which is obtainable from the usual reaction diffusion equation and multiwave solutions, it is not possible to obtain any fluctuation wave branch like that given in ref. [2]. We note that, due to the large difference between the spatial scales of chemical reaction and diffusion, it is doubtful to use the multivariate master equation in analysing the critical behaviour of non-linear system.