The stability analysis of a cometary ionosphere by Ershkovich, Mchenzie, and Axford is extended to include the effects of plasma motion. In the local inertial frame of reference moving with the plasma we arrived at the same instability criterion, but the Brunt-Vaisala frequency which governs the convective instability now involves the centrifugal force which has a destabilizing effect. As a result, the unstable becomes broader, expanding to greater distances from the ionopause. An increase of the comet production rate is shown to stabilize the ionosphere whereas an increase of the ion-neutral momentum exchange rate has a destabilizing effect. The cometary ionopause is shown to undergo the convective instability