We present the exact solution of the kinetic and electromagnetic equations for a large-amplitude plane magnetoacoustic wave propagating transverse to the magnetic field in a hot collisionless plasma. The solution gives simple relations amoung the magnetic field strength, density, stress tensor and plasma velocity, all of which are measurable in the interplanetary plasma. these relations are independent of the electron and ion velocity distributions, subject to certain restrictions on 'high-velocity tails.' The magnetic field of the wave is linearly polarized. The wave steepens to form a shock much as the analogous waves of MHD theory do.