  We calculate the ratios of $B$ and $D$ meson decay constants by applying the
variational method to the relativistic hamiltonian of the heavy meson. We adopt
the Gaussian and hydrogen-type trial wave functions, and use six different
potentials of the potential model. We obtain reliable results for the ratios,
which are similar for different trial wave functions and different potentials.
The obtained ratios show the deviation from the nonrelativistic scaling law,
and they are in a pretty good agreement with the results of the Lattice
calculations.
