A relativistic theory for a nonlinear magnetosonic wave propagating perpendicularly to a magnetic field is developed. On the basis of a relativistic two‐fluid cold plasma model, the structure of a stationary magnetosonic wave is studied. Relativistic effects become important for the parameter regime &ohgr;ce/&ohgr;pe≳1, because the fluid electron velocity perpendicular to a magnetic field and parallel to the wave front takes values close to the speed of light for such plasma parameters. It is found that there exists a stationary solitary wave solution even in the relativistic model. Some properties of the solitary wave, such as the soliton width, are discussed.