  In the framework of the extended $SU(2)_{h}\times SU(2)_{l}$ model we study
the radiative decay of an extra gauge boson $Z^{\prime}$, $Z^{\prime}\to\gamma
Z$. The data analysis results of the CDF collaboration at the Fermilab Tevatron
allow one to establish not only the lower bound of the decay probability
$Z^{\prime}\to\gamma Z$ normalized to Drell-Yan process $Z^{\prime}\to
\mu^{+}\mu^{-}$, $R(Z^{\prime}\to\gamma Z/\mu^{+}\mu^{-})> 1.4\times
10^{-5}\cot^{2}\phi$, but also to estimate the mixing angle $\xi$ between the
states $Z^{\prime}$ and $Z$, $|\xi| < 5\times 10^{-2}$, taking into account the
additional mixing angle $\phi$ related to the extended gauge group
$SU(2)_{h}\times SU(2)_{l}$. The comparison with the decays
$Z^{\prime}\to\tau^{+}\tau^{-}$ and $Z^{\prime}\to \bar b b$, $Z^{\prime}\to
\bar t t$ based on the LEP data is also presented.
