Propagation of magnetostatic surface waves (MSSWs) in a ferrite plate magnetized by a spatially periodic transverse field has been considered. The parameters of MSSW propagation have been calculated by the Hamilton-Auld method. It is shown that only noncollinear MSSWs, whose wave-beam trajectories as well as wave numbers and angles, which determine the directions of the vectors of the phase and group velocities, are described by functions that are periodic in the direction of the wave propagation, can exist in this field. The period of these functions is determined by the period of the spatially periodic field. The frequency range of existence of the collinear waves is narrower than that of the waves in a uniformly magnetized plate. The characteristics of wave propagation in a nonuniform spatially periodic field are compared to the characteristics of wave propagation in nonuniform fields of known types.