[en] We have computed the decay constants for the B and D mesons, using quenched lattices at β = 6.3, by interpolating between the static approximation of Eichten and the conventional (''heavy'' Wilson fermion) method. A more careful treatment of the static result using better sources with longer time-displacements and a modification to the Wilson quark normalization to correct approximately for lattice effects in the large-am regime have led to the elimination of the large discrepancy between the two methods which had been previously observed. We report final results, with estimates of various systematic errors