  In this paper, the width of the decay $\tau \rightarrow
K^{-}\pi^{0}\nu_{\tau}$ is calculated in the framework of the
Nambu-Jona-Lasinio model. The contributions of the intermediate vector
$K^{*}(892)$ and scalar $K_{0}^{*}(800)$ mesons are taken into account. It is
shown that the main contribution to the width of this decay is given by the
subprocesses with the intermediate $W$-boson and vector $K^{*}(892)$ meson. The
scalar channel with the intermediate $K_{0}^{*}(800)$ meson gives an
insignificant contribution. In Appendix, it is shown that the contribution of
the subprocess with the intermediate ${K^{*}}'(1410)$ meson is negligible as
well. The obtained results are in satisfactory agreement with the experimental
data.
