It is interesting to study the characteristics of the whole family of B c which contains two different heavy flavors. LHC and the proposed Z 0 factory provide an opportunity because a large database of the B c family will be achieved. B c and its excited states can be identified via their decay modes. As suggested by experimentalists, B * c (ns) → B c + γ is not easy to be clearly measured, instead, the trajectories of π + and π − occurring in the decay of B c (ns) → B c (ms) + π + π − ( n > m ) can be unambiguously identified, thus the measurement seems easier and more reliable; therefore this mode is more favorable at the early running stage of LHCb and the proposed Z 0 factory. In this work, we calculate the rate of B c (ns) → B c (ms) + π + π − in terms of the QCD multipole-expansion and the numerical results indicate that the experimental measurements with the luminosity of LHC and Z 0 factory are feasible. meson, hadronic decay, QCD multipole-expansion 12.38.Bx