A theoretical analysis was carried out to determine the stability properties of unsteady natural convection. In this analysis a perturbation technique was used in conjunction with a special type unsteady base flow for transient natural convection between two infinite parallel vertical plates. Perturbation analysis yields a sequence of ordinary differential equations to describe the coupled time‐dependent disturbance behavior. The equations were solved for a number of values of Grashof and wavenumbers and for a wide range of rate of acceleration and deceleration to determine the unsteady base flow stability characteristics. A growth factor was used to determine the stability properties, and it was found that an accelerating (decelerating) base flow is more (less) stable than a steady base flow when compared at common values of the instantaneous Grashof number. This tendency was found to increase rapidly at first and then to slowly decrease with increasing rate of change of the base flow.