IT WAS realized as early as 1906(1) that coupling between an autocatalytic reaction and the diffusion of the autocatalytic component can give rise to a propagating reaction front-a chemical wave. Chemical waves have been studied intensively in fluid-phase reaction-diffusion systems(2), but in recent years a variety of spatiotemporal patterns has also been observed for oscillatory reactions on single-crystal surfaces(3,4). One important new aspect that has been introduced by these studies is that of anisotropic diffusion, as a consequence of the fixed surface geometry on which the diffusion of the adsorbed particles takes place. Here we report the observation of a transition from elliptical to square-shaped concentric chemical waves in the reaction of NO and H-2 On a rhodium(110) surface. The elliptical pattern is characteristic of simple anisotropic diffusion, but we attribute the origin of the square pattern to a state-dependent anisotropy-that is an anisotropy that varies along the wave profile as changes in the adsorbate coverage generate different reconstructions of the substrate structure. This interplay between diffusional anisotropy and the state of the system can be expected to be quite general and to give rise to new varieties of oscillatory patterning.