  In the extended Nambu--Jona-Lasinio model, the decay widths of the processes
$\tau \to [\omega(782), \phi(1020)] K^{-} \nu_{\tau}$ were calculated. The
intermediate strange quark-antiquark mesons in both the ground and the first
radially excited states were taken into account. The meson $K_{1}(1400)$, being
a possible candidate for the role of the tetraquark meson, was also taken into
account as an intermediate state. The result for the process $\tau \to
\omega(782) K^{-} \nu_{\tau}$ is in satisfactory agreement with the
experimental data. Simultaneously, the result for the decay $\tau \to
\phi(1020) K^{-} \nu_{\tau}$ is in agreement with the experimental data with
precision $1.3 \sigma$.
