The anisotropic diffusion of ions and electrons in a nonmultiplying partially ionized plasma lying in a strong uniform magnetic field has been analyzed to zero and first order in the parameter &OHgr;−1, where &OHgr;2is the ratio of the reduction of transverse electron mobility to the reduction of transverse ion mobility due to the magnetic field. This obviates the need for an earlier erroneous assumption. Potential distribution and electron and ion current flows have been formulated for two‐dimensional flow, using a lowest‐harmonic charged‐particle distribution in a rectangular space and various wall‐current conditions. The encroachment of sheaths inward from the walls has not been considered on the basis that, in principle, the charged‐particle concentration could always be assumed to be large enough to keep this complication small.