  The double ratio $(f_{B_s}/f_{B_d})/(f_{D_s}/f_{D_d})$ is calculated by QCD
sum rules in heavy quark effective theory (HQET), both numerically and
analytically. Our expression for the double ratio shows explicitly the
dependence on the light quark masses, the heavy quark symmetry breaking and the
vacuum condensates. The numerical result favors the double ratio to be a little
greater than 1.
