An exact solution of the Vlasov equations is presented, describing a plasma layer confined between two regions of oppositely directed magnetic fields. Electrons and ions have Maxwellian distributions at the plane where the magnetic field is zero. In a coordinate system where the electron and ion drift velocities are equal in magnitude but opposite in direction, the electric field vanishes and the electron and ion densities are equal throughout. In a recent paper, MJOLNESS, RIBE, and RIESENFIELD found a solution of the Vlasov equations describing a plasma sheath separating regions of oppositely directed magnetic fields. This solution was useful in interpreting experimental results from fast azimuthal pinch experiments. The solution was based on approximations, including the assumption that ions move only under the influence of the electric field, the ion current is neglected, and the electron and ion densities are equal. This solution is similar to that found by ROSENBLUTH and GARWIN. A similar solution was previously found by the author but was not published. This solution differs significantly from the one found by MJOLNESS et al. It does not require any approximations and is exact. A continuous distribution of velocities is assumed, and the velocity distributions are Maxwellian at the plane where the magnetic field is zero. Due to these differences and the current interest in sheaths, it is worth providing a brief account of this work. The Vlasov equations are solved, with the equations describing the motion of particles in electromagnetic fields. The solution assumes that E has only an x-component and B has only a z-component. The vector potential is taken to have only a y-component. The equations are rearranged to facilitate the solution.An exact solution of the Vlasov equations is presented, describing a plasma layer confined between two regions of oppositely directed magnetic fields. Electrons and ions have Maxwellian distributions at the plane where the magnetic field is zero. In a coordinate system where the electron and ion drift velocities are equal in magnitude but opposite in direction, the electric field vanishes and the electron and ion densities are equal throughout. In a recent paper, MJOLNESS, RIBE, and RIESENFIELD found a solution of the Vlasov equations describing a plasma sheath separating regions of oppositely directed magnetic fields. This solution was useful in interpreting experimental results from fast azimuthal pinch experiments. The solution was based on approximations, including the assumption that ions move only under the influence of the electric field, the ion current is neglected, and the electron and ion densities are equal. This solution is similar to that found by ROSENBLUTH and GARWIN. A similar solution was previously found by the author but was not published. This solution differs significantly from the one found by MJOLNESS et al. It does not require any approximations and is exact. A continuous distribution of velocities is assumed, and the velocity distributions are Maxwellian at the plane where the magnetic field is zero. Due to these differences and the current interest in sheaths, it is worth providing a brief account of this work. The Vlasov equations are solved, with the equations describing the motion of particles in electromagnetic fields. The solution assumes that E has only an x-component and B has only a z-component. The vector potential is taken to have only a y-component. The equations are rearranged to facilitate the solution.