  We study the rare hadronic transitions $\Upsilon(2S)\rightarrow
\Upsilon(1S)\eta$ and $\Upsilon(2S)\rightarrow \Upsilon(1S)\pi^0$ using a
sample of 158 $\times 10^6$ $\Upsilon(2S)$ decays collected with the Belle
detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We observe the
$\eta$ meson decay to $\gamma\gamma$ and $\pi^+\pi^-\pi^0$ final states; the
$\Upsilon(1S)$ is reconstructed in the $\mu^+\mu^-$ and $e^+e^-$ decay modes.
We measure the ratios of branching fractions (${\mathcal B}$) $\frac{{\mathcal
B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\eta)}{{\mathcal
B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\pi^+\pi^-)}$ = (1.99$\pm$0.14 (stat)
$\pm$0.11 (syst)) $\times 10^{-3}$ and
  $\frac{{\mathcal B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\pi^0)}{{\mathcal
B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\pi^+\pi^-)} < 2.3 \times 10^{-4}$ at the
90% confidence level (CL). Assuming the value ${\mathcal B}(\Upsilon(2S)
\rightarrow \Upsilon(1S)\pi^-\pi^+)$ = (17.92$\pm$0.26)%, we obtain $ {\mathcal
B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\eta) = (3.57 \pm 0.25 ({\rm stat})\ \pm
0.21 ({\rm syst}))\times 10^{-4} $ and $ {\mathcal
B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\pi^0) < 4.1\times 10^{-5}\ ({\rm 90%\
CL}). $
