  Recently, the deviation of the ratios $R(D)$, $R(D^{*})$ and $R(J/\psi)$ have
been found between experimental data and the Standard Model predictions, which
may be the hint of New Physics. In this work, we calculate these ratios within
the Standard Model by using the improved instantaneous Bethe-Salpeter method.
The emphasis is pad to the relativistic correction of the form factors. The
results are $R(D)=0.312 ^{+0.006}_{-0.007}$, $R(D^*)= 0.249^{+0.001}_{-0.002}$,
$R(D_s)=0.320 ^{+0.009}_{-0.009}$, $R(D^*_s)=0.251 ^{+0.002}_{-0.003}$,
$R(\eta_c)=0.384 ^{+0.032}_{-0.042}$, and $R(J/\psi)=0.267 ^{+0.009}_{-0.011}$,
which are consistent with predictions of other models and the experimental
data. The semileptonic decay rates and corresponding form factors at zero
recoil are also given.
