The instability induced by a vertical external gravitational field in a stratified plasma permeated by a uniform horizontal magnetic field is investigated by means of an expansion method. Dissipative processes arising from finite electrical and thermal conductivities are considered. It is found that a new unstable mode exists and a new condition, in addition to the Schwarzschild condition, must be satisfied for stability. The new stability condition is associated with the modes which exist in the nondissipative plasma, but are modified by dissipation. The net effect of this new condition is to destabilize the system.