The laminar free convection problem of a flat plate which is hung vertically in the air is solved, taking into account the variation of properties of air which depends on temperature. Previously the author solved the same problem by perturbation theory using ε=(T₀-T₁)/T₁ as a small parameter, where T₀ and T₁ are the absolute temperatures of the surface and the surrounding air, respectively. In this report the rigorous solution for a larger value of ε(=2.0 and 4.0) by successive approach method is presented. The heat-transfer coefficient can be expressed as follows : α=α_ε=0(1-0.055ε)