  Considering a self-interaction only of mirror fermions in the context of a
lattice-regularized fermion field theory, we show that the system undergoes
spontaneous breaking of chiral symmetry and mirror-fermion masses are
generated. However, it is explicitly shown that there are no Goldstone bosons
appearing together with this spontaneous symmetry breaking phenomenon, since
Lorentz invariance, one of very general prerequisites of the Goldstone theorem,
is violated. The result and its possible application are briefly discussed.
