  The branching fraction of the decay $\tau \to K^{-} \eta \nu_{\tau}$ has been
calculated by using the extended Nambu-Jona-Lasinio model taking into account
the meson interaction in the final state. The contact term and the channel with
the intermediate ground $K^{*}(892)$ and first radially excited state
$K^{*}(1410)$ have been calculated. For the purpose of describing the meson
interaction in the final state, the triangle diagram with three mesons has been
considered. The cutoff parameter of divergent integrals of the meson loop is
equal to the appropriate parameter used in our previous work to describe the
decay $\tau \to K^{-} \pi^{0} \nu_{\tau}$. Thereby, the present work does not
set any additional arbitrary parameters. The obtained results are in
satisfactory agreement with the experimental data.
