The onset of natural convection in a horizontal fluid layer cooled from above is investigated theoretically. The initially quiescent fluid placed between two flat plates is cooled by decreasing the upper boundary temperature at a constant time-rate. Its stability analysis is conducted by employing the propagation theory, which considers variations of disturbances with the time upon their onset. The critical conditions predicted by this theory are found agree favorably with the existing experimental results. Also, the effect of the Prandtl number on instability is discussed.