The onset of surface-tension-driven convection in an initially quiescent liquid layer experiencing sudden desorption from a free surface is analyzed using the linear stability theory. The propagation theory was developed for the basic time-dependent concentration profile, which is strongly nonlinear. Based on this theory, a new set of stability equations is derived in considering the effect of Gibbs adsorption and by neglecting the surface diffusion. It is found that the liquid layer becomes more stable by decreasing the Schmidt and Biot numbers. It is interesting that, during an initial period the system is stable, depending on the Gibbs effect. The predictions agree favorably with the existing experimental results of triethylamine desorption in water in a wetted-wall and a liquid-jet column.