  We analyze the semileptonic (B_c -> B_u* l+ l-) decay in the frame work of
the Standard Model. We calculate the (B_c) to (B_u*) transition form factors in
QCD sum rules. Analytical expressions for the spectral densities and gluon
condensates are presented. The branching ratio of the (B_c -> B_u* l+ l-) decay
is calculated, and it is obtained that this decay can be detectable at
forthcoming LHC machines.
