  We study the $B_C$ meson rare decay in order to search for the Majorana
neutrino signal. It is found that the the corresponding decay rate is sensitive
to the Majorana neutrino mass and mixing angles. The signal of $B_C^\pm\to
l_1^\pm l_2^\pm M^\mp $ induced by the Majorana neutrino within the mass region
$m_\pi<m_n<m_B$ may be observed at LHCb.
