The presence of magnetically reflected particles is shown to allow the existence of large amplitude magnetosonic solitary waves in relativistic electron–positron plasmas. If the flow is assumed to contain a single loop of gyrating particles, self‐consistent structures are found with peak field amplitudes (B/B∞)max<(11)1/2, whereB∞is the magnitude of the upstream magnetic field. In contrast, without reflected particles, the amplitude of a relativistic magnetosonic soliton is restricted to (B/B∞) −1<2/&ggr;∞, where &ggr;∞is the upstream Lorentz factor. Therefore, if &ggr;∞≫1, reflected particles greatly increase the allowable amplitudes of these nonlinear waves. It is also shown that when &ggr;∞≫1, the wave properties are independent of &ggr;∞, and are completely parametrized by the ratio of the Poynting flux to the kinetic energy flux in the upstream flow. Some new features of solitary waves without reflected particles are also derived, and a heuristic model is presented which gives a simple physical interpretation of many of these results.