The stability of the double-diffusive convection of a binary solution unidirectionally solidified from above, a freckle-free system, is investigated analytically. Results show that, interestingly, the stability characteristics of the double-diffusive convection resemble those of thermal convection in a similar system. This conclusion is reached on the basis of the following results: First, the neutral curve is invariably uni-modal. Secondly, the critical Rayleigh number increases linearly with the viscosity contrast coefficient γ (defined in Eq. (14)). Thirdly, the onset of convection is confined to the region below a stagnant lid of thickness In γ * (defined in Section 5.3). Finally, the stability characteristics of the convection are significantly influenced by the viscosity variation, the Prandtl number, and the temperature of bulk fluid, the three parameters influential on the thermal boundary layer thickness; other physical parameters, such as the Darcy number of the mushy zone, the concentration ratio, and the Stefan number, corresponding with the variation of the morphology of the mush, have relatively insignificant effect on the stability of convection. All the above four facets also hold for the thermal convection of the system in which a pure fluid is solidified from above. This resemblance explains why the present cooling-from-above system is freckle-free.