  The stability of a Fermi ball (F-ball), which is a kind of non-topological
soliton accompanying the breakdown of the approximate $Z_2$ symmetry, is
investigated in three situations: the case it is electrically neutral, the case
it is electrically charged and unscreened, and the case it is electrically
charged and screened. We argue only the third case is physically meaningful
since the neutral F-ball is unstable and the case of the unscreened charged one
is observationally excluded when it has a sizable contribution to CDM. We found
that the energy scale of the breakdown of the approximate $Z_2$ symmetry $v$
should satisfy $v<3\times 10^6 {GeV}$ if the F-ball is a main component of CDM.
