  We report the first measurement of the Michel parameter $\xi^\prime$ in the
$\tau^-\to\mu^-\bar{\nu}_\mu\nu_\tau$ decay with a new method proposed just
recently. The measurement is based on the reconstruction of the
$\tau^-\to\mu^-\bar{\nu}_\mu\nu_\tau$ events with subsequent muon
decay-in-flight in the Belle central drift chamber. The analyzed data sample of
$988\,\text{fb}^{-1}$ collected by the Belle detector corresponds to
approximately $912\times10^6$ $\tau^+ \tau^-$ pairs. We measure
$\xi^\prime=0.22\pm0.94(\text{stat})\pm0.42(\text{syst})$, which is in
agreement with the standard model prediction of $\xi^\prime=1$. Statistical
uncertainty dominates in this study, being a limiting factor, while systematic
uncertainty is well under control. Our analysis proved the practicability of
this promising method and its prospects for further precise measurement in
future experiments.
