Since Yang [Phys. Rev. Lett 63 (1989) 21441 proposed the possible exis
tence of the eta-pairing off-diagonal long-range order (ODLRO) in the
ground states of the negative-U Hubbard model, this problem has been s
tudied by many physicists. In this article, based on our previous work
, we shall rigorously show that all the ground states, which have the
eta-pairing ODLRO, are actually supersolid rather than superfluid as o
ne expected before.