A general solution to nonsteady coupled magnetohydrodynamic plane Couette flow by the method of Fourier series expansion is presented in this paper. Two particular examples of the utility of the solution are included: 1) an impulsive start of the wall, and 2) a wall velocity proportional to (1 − exp(− αt)). For the case of an impulsive start of the wall it is found that flow is apparently accelerated by the presence of the magnetic field, a situation opposite to that which occurs when no induced magnetic field is allowed.