  We re-calculate the exclusive semileptonic and nonleptonic decays of $B_c$
meson to a $P$-wave charmonium in terms of the improved Bethe-Salpeter (B-S)
approach, which is developed recently. Here the widths for the exclusive
semileptonic and nonleptonic decays, the form factors, and the charged lepton
spectrums for the semileptonic decays are precisely calculated. To test the
concerned approach by comparing with experimental measurements when the
experimental data are available, and to have comparisons with the other
approaches the results obtained by the approach and those by some approaches
else as well as the original B-S approach, which appeared in literature, are
comparatively presented and discussed.
