  We extend our recent work, in which the Dirac equation with a
``(asymptotically free) Coulomb + (Lorentz scalar $\gamma_0\sigma r$) linear ''
potential is used to obtain the light quark wavefunction for $q\bar Q$ mesons
in the limit $m_Q\to \infty$, to estimate the decay constant $f_P$ and the
mixing parameter $B$ of the pseudoscalar mesons. We compare our results for the
evolution of $f_P$ and $B$ with the meson mass $M_P$ to the non-relativistic
formulas for these quantities and show that there is a significant correction
in the subasymptotic region. For $\sigma =0.14{{\rm ~GeV}}^{-2}$ and $\lms
=0.240{\rm ~GeV}$ we obtain: $f_D =0.371\; ,\; f_{D_s}=0.442\; ,\; f_B=0.301\;
,\; f_{B_s}=0.368 {\rm ~GeV}$ and $B_D=0.88\; ,\; B_{D_s}=0.89\; ,\; B_B=0.95\;
,\; B_{B_s}=0.96\; ,\;$ and $B_K=0.60$.
