Dense suspensions of magnetotactic bacteria form long, thin, stable bands perpendicular to the common, net direction of motion of the cells in a magnetic field. A mechanism for this phenomenon is proposed in which the hydrodynamic coupling between two swimming cells is described in terms of an approximate, far-field solution for the flow around one swimming cell. The calculated hydrodynamic interaction force and torque based upon this analysis are of the correct orders of magnitude and in the right directions to provide a reasonable explanation for band formation and stability.