A sheared flow equilibrium in the magnetosphere-ionosphere (M-I) coupling system and its stability against the Kelvin-Helmholtz (K-H) instability are investigated within the ideal MHD by using a box-shaped magnetospheric model. Without forcing, the unperturbed transverse (convection) electric field responsible for the E¿B drift declines exponentially with time due to the ionospheric Joule dissipation and the decay (e-folding) time is larger than one-half of the Alfv¿n bounce period. The restoring force due to the line bending associated with the transverse magnetic field is responsible for the existence of a critical height-integrated Pedersen conductivity &Sgr;Pc~(&mgr;0VA)-1, where VA is the average Alfv¿n velocity along the field line, above which the K-H instability in the magnetosphere is suppressed completely. ¿ American Geophysical Union 1996