Abstract: The stability problem of rotating parallel flows was discussed by use of the barotropic vorticity equation. A stability criterion of barotropic stability was obtained. It is an explicit expression which relates the perturbation growth rate to the function of the energy conversion between basic motion and perturbation. The results indicate that the growth rate of pertubation is proportional to that of the energy conversion. In addition, the case of a basic flow with horizontal linear shear was treated for β≠0. Some results obtained are similar to that given by Haltiner(1971) for β=0. The perturbations are damped waves. The wave speed, however, has a westward component which depends upon the strength of the shear of basic f lows.