Starting with the Chew, Goldberger & Low equations, an analysis is made of instability arising due to a tangential velocity discontinuity in a dilute plasma. The velocities on either side are parallel but oppositely directed. Two cases are considered: (i) the magnetic field is uniform and everywhere transverse to the motion, and (ii) the magnetic field vectors on either side are orthogonal, being parallel to the motion on one side and perpendicular on the other. The conditions for instability are obtained and it is found that the effect of magnetic field is destabilizing in both cases. The effect of orthogonality of magnetic fields on the conventional fire-hose instability for a uniform, static plasma is also discussed as special case.