Z₆ symmetry of the Standard Model and Technicolor theory

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.