  We predict the masses of the lowlying $B_c$ mesons with $J^P =
0^-,\,1^-,\,0^+,\,1^+,\,2^+$, using a flavor dependent interaction pattern
which gives an unified successful description of the light, heavy-light and
heavy mesons and is also appliable to the radial excited heavy mesons. The
errors are controlled carefully. With the errors from the RL approximation
subduced, our predictions are consistent with the lQCD and quark model results,
which supports strongly that the flavor dependent interaction pattern is
reasonable. Our predictions provide significant guides to the experiment search
of the $B_c$ mesons.
