  We present a measurement of the Michel parameters of the $\tau$ lepton,
$\bar{\eta}$ and $\xi\kappa$, in the radiative leptonic decay $\tau^-
\rightarrow \ell^- \nu_{\tau} \bar{\nu}_{\ell} \gamma$ using
711~f$\mathrm{b}^{-1}$ of collision data collected with the Belle detector at
the KEKB $e^+e^-$ collider. The Michel parameters are measured in an unbinned
maximum likelihood fit to the kinematic distribution of
$e^+e^-\rightarrow\tau^+\tau^-\rightarrow (\pi^+\pi^0
\bar{\nu}_\tau)(\ell^-\nu_{\tau}\bar{\nu}_{\ell}\gamma)$ $(\ell=e$ or $\mu)$.
The measured values of the Michel parameters are $\bar{\eta} = -1.3 \pm 1.5 \pm
0.8$ and $\xi\kappa = 0.5 \pm 0.4 \pm 0.2$, where the first error is
statistical and the second is systematic. This is the first measurement of
these parameters. These results are consistent with the Standard Model
predictions within their uncertainties and constrain the coupling constants of
the generalized weak interaction.
