  We show that there are two reasons why the partial width for the transition
$\Gamma_1(\Upsilon(3S)\rightarrow \gamma\chi_{b1}(1P))$ is suppressed. Firstly,
the spin-averaged matrix element (m.e.) $\bar{I(3S|r|1P_J)}$ is small, being
equal to 0.023 GeV$^{-1}$ in our relativistic calculations. Secondly, the
spin-orbit splittings produce relatively large contributions, giving
$I(3S|r|1P_2)=0.066$ GeV$^{-1}$, while due to large cancellation the m.e.
$I(3S|r|1P_1)=-0.020$ GeV$^{-1}$ is small and negative; at the same time the
magnitude of $I(3S|r|1P_0)=-0.063$ GeV$^{-1}$ is relatively large. These m.e.
give rise to the partial widths: $\Gamma_2(\Upsilon(3S)\rightarrow
\gamma\chi_{b2}(1P))=212$ eV, $\Gamma_0(\Upsilon(3S)\rightarrow
\gamma\chi_{b0}(1P))=54$ eV, which are in good agreement with the CLEO and
BaBar data, and also to $\Gamma_1(\Upsilon(3S)\rightarrow
\gamma\chi_{b1}(1P))=13$ eV, which satisfies the BaBar limit, $\Gamma_1(exp.) <
22$ eV.
