  The spectrum and relativistic wave functions of $B_c$ system are investigated
via solving the complete Salpeter equation. Emphases are put on the study of
the partial waves of each $J^P$ state. Our study shows that there are three
categories of $J^P$ states. The first category contains $0^-$ and $0^+$ states,
which are ${}^1S_0$ dominant state with a small amount of $P$ wave and
${}^3P_0$ dominant state with a small amount of $S$ wave, respectively. The
second category includes the natural parity states, such as $1^-$, $2^+$,
$3^-$, etc. Taking the $1^-$ state as an example, we study it in two cases. One
is the ${}^3S_1$ dominant state with a small amount of $P$ and $D$ waves, and
the other is the ${}^3D_1$ dominant state but contains a large amount of $S$
and $P$ wave components. The third category includes the unnatural parity
states, such as $1^+$, $2^-$, $3^+$, etc. For the $1^+$ spectrum, the states
are grouped into pairs with different radial quantum numbers. Each pair
contains two ${}^1P_1-{}^3P_1$ mixing states, and the corresponding mixing
angles are calculated by using the relativistic wave functions.
