The stability of an electrically conducting fluid flowing between parallel planes subject to a transverse magnetic field is investigated for infinitesimal three‐dimensional disturbances. Primary interest is in the effect of the magnetic field on the critical point of the neutral stability curves. The governing stability equations include perturbations for both the velocity and magnetic fields and result in a sixth‐order coupled set of linear differential equations. The results indicate a strong dependence of the critical eigenvalues on both the magnetic field strength and a fluid property, the magnetic Prandtl number. The effect of both is to stabilize the flow.