The self-consistent effective binary diffusion (SCEBD) approximation for multicomponent diffusion in gas mixtures is reconsidered and reformulated. The new formulation is based on the fact that a suitable rearrangement of the Stefan-Maxwell equations provides an exact expression for the complementary mean velocity ai for species i as a weighted average of the velocities of all the other species. The coefficients in ai are normalized friction coefficients which are simply related to the true binary diffusion coefficients. A simple factorized bilinear approximation to the friction coefficients then yields approximate species diffusion fluxes identical in form to those of a previous intuitive treatment [4], together with a new relation between the previously ambiguous weighting factors wi and the friction coefficients. This relation places the SCEBD approximation on a firm foundation by providing a rational basis for determining the wi . A simple further approximation based on the known form of the friction coefficients for hard spheres yields wi = (const.)ρi/{sqrt}Mi, where ρi and Mi are respectively the mass density and molecular weight of species i. These weighting factors are shown to produce considerably more accurate diffusion velocities than the conventional choice wi = (const.) ρi/Mi.