  We have measured branching fractions of hadronic $\tau$ decays involving an
$\eta$ meson using 485 fb^{-1} of data collected with the Belle detector at the
KEKB asymmetric-energy e^+e^- collider. We obtain the following branching
fractions: ${\cal B}(\tau^-\to K^- \eta \nu_{\tau})=(1.62\pm 0.05 \pm
0.09)\times 10^{-4}$, ${\cal B}(\tau^-\to K^- \pi^0 \eta \nu_{\tau}) =(4.7\pm
1.1 \pm 0.4)\times 10^{-5}$, ${\cal B}(\tau^-\to \pi^- \pi^0 \eta
\nu_{\tau})=(1.39 \pm 0.03 \pm 0.07) \times 10^{-3}$, and ${\cal B}(\tau^-\to
K^{*-} \eta \nu_{\tau})=(1.13\pm 0.19 \pm 0.07)\times 10^{-4}$ improving the
accuracy compared to the best previous measurements by factors of six, eight,
four and four, respectively.
