Spatially periodic structures of a parameterized fourth order reaction-diffusion system with-diffusion instability, where the diffusion term is governed by Cahn-Hillard's generalized diffusion law, are studied by means of bifurcation theory. A criterion of bifurcation for generating ipatially periodic steady states from spatially homogeneous steady states is provided through stability and singularity analysis. The second order approximation of spatially periodic steady states. is obtained by singular perturbation technique. The theoretical results in this paper are in good accord ance with numerical results in [3] .