A generalization of the phenomenological description of ambipolar diffusion of a plasma is made to include the effects of a weak impressed magnetic field. The assumptions of congruence of the flow vectors (div &Ggr;+= div &Ggr;−) for ions and electrons and of proportionality [n−grad (n+) =n+grad (n−)] on the signed charge densities are utilized as in the existing theory of ambipolar diffusion; however, because of the rotational effects of the magnetic field, and additional assumption is made on the curls of &Ggr;±. This assumption is curl &Ggr;+= curl &Ggr;−. The resulting diffusion is found to be a combination of electronic and ionic diffusion, and the components of the ambipolar diffusion tensor are calculated for a unidirectional magnetic field.