The present work represents a significant improvement on our earlier work dealing with the formulation of a kinetic equation for a plasma in a "strong" static magnetic field B. Here without making any assumptions concerning the isotropy of the one- and two-particle distribution functions in the plane perpendicular to the magnetic field, a kinetic equation is derived in which the collision term is valid to all orders in 1/B and takes complete account of the effect of the strong magnetic field on the collisions.