  We consider the possibility to continue the $Z_6$ symmetry of the Standard
Model to the Technicolor theories. Among the SU(N) Weinberg - Susskind models
and the SU(N) Farhi - Susskind models for $N>2$ only the SU(4) Farhi - Susskind
model may possess the mentioned symmetry. We also show that the hypercharge
assignment of Minimal Walking SU(2) Technicolor model may be chosen in such a
way that the additional discrete symmetry is preserved.
