  The lepton number violating process, $e^- e^- \to W^- W^-$ has been widely
discussed in the Majorana neutrino exchange mechanism. Here, we discuss this
process in a composite neutrino model where excited Majorana neutrinos are
exchanged. We found several qualitatively different features from the neutrino
exchange case: (1) The longitudinally polarized $W$'s are not produced, (2) the
neutrinoless double beta decay does not constrain much and a much larger cross
section is expected, and (3) CP violating phases may be explored because all
excited neutrinos are heavy so that large mixings among them are expected.
