  The $\eta$ transitions of $\Upsilon(4S,5S)$ into $\Upsilon(1S,2S)$ are
studied in the rescattering model by considering the final state interactions
above the $B\bar B$ threshold. The width of the $\eta$ transition of
$\Upsilon(4S)$ into $\Upsilon(1S)$ is found to be larger than that of the
dipion transition, and the ratio of $\Gamma(\Upsilon(4S)\to\Upsilon(1S)\eta)$
to $\Gamma(\Upsilon(4S)\to\Upsilon(1S)\pi^+\pi^-)$ is predicted to be
$R_4=1.8{-}4.5$, which is about two orders of magnitude larger than the
expectation of the conventional hadronic transition theory, and is supported by
the new BaBar measurement. The widths of the $\eta$ transitions of
$\Upsilon(5S)$ are found to be sensitive to the coupling constants
$g_{\Upsilon(5S)B^{(*)}B^{(*)}}$ due to a large cancelation between
contributions from the $B\bar{B}$, $B^*\bar{B}+c.c.$, and $B^*\bar{B}^*$
channels, and only a rough estimate
$\Gamma(\Upsilon(5S)\to\Upsilon(1S,2S)\eta)=10{-}200$ KeV can be given. The
widths of the $\eta'$ transitions of $\Upsilon(4S,5S)$ are also discussed, and
they could be much smaller than that of the corresponding $\eta$ transitions
mainly due to the tiny phase space.
