  An alternative pattern of the chiral symmetry breaking, suggested recently by
Stern, is investigated. It could be self-consistent provided that the chiral
$SU(N_f) \times SU(N_f)$ symmetry is broken spontaneously down to $SU(N_f)
\times Z_{N_f}$ rather than to $SU(N_f)_V$. The discrete axial $Z_{N_f}$ then
would play a custodial role preventing the quark bilinears from condensation.
It is shown that this pattern of the chiral symmetry breaking is ruled out in
QCD by exact inequalities. It is not ruled out, however, in other gauge
theories with scalar quarks and/or Yukawa couplings.
