  Using data collected in the Belle experiment at the KEKB asymmetric-energy
$e^+e^-$ collider we search for transitions $\Upsilon(4S) \rightarrow
\eta_b(1S)\omega$, $\Upsilon(5S) \rightarrow \eta_b(1S)\omega$ and
$\Upsilon(5S) \rightarrow \eta_b(2S)\omega$. No significant signals are
observed and we set 90\% confidence level upper limits on the corresponding
visible cross sections: $0.2 ~\textrm{pb}, 0.4 ~\textrm{pb}$ and $1.9
~\textrm{pb}$, respectively.
