  Operating just once with the naive Foldy-Wouthuysen-Tani transformation on
the relativistic Fermi-Yang equation for $Q\bar q$ bound states described by
the semi-relativistic Hamiltonian which includes Coulomb-like as well as
confining scalar potentials, we have calculated heavy meson mass spectra of D
and B together with higher spin states. Based on the formulation recently
proposed, their masses and wave functions are expanded up to the second order
in $1/m_Q$ with a heavy quark mass $m_Q$ and the lowest order equation is
examined carefully to obtain a complete set of eigenfunctions for the
Schr\"odinger equation. Heavy quark effective theory parameters, $\bar\Lambda$,
$\lambda_1$, and $\lambda_2$, are also determined at the first and second order
in $1/m_Q$.
