  We show that the $\eta\gamma Z$ anomaly can be measured by analysing
parity-violating effects in the $\eta-->\gamma\mu+\mu-$ decay. In this sense,
we find that the longitudinal polarization of the outgoing $\mu^+$ is an
appropriate observable to be considered in future high-statistics $\eta$
factories. The effect is expected to lie in the range $10^{-5}-10^{-6}$ in the
Standard Model.
