  The direct production rate of $\psi$ in the $\Upsilon$ decay is shown to be
dominated by the process $ \Upsilon \to ggg^*$ followed by $g^* \to \psi$ via
the color-octet mechanism proposed recently to explain the anomalous prompt
charmonium production at the Tevatron. We show that this plausibly dominant
process has a branching ratio compatible with the experimental data. Further
experimental study in this channel is important to test the significance of the
color-octet component of $c\bar c$ pair inside the $\psi$ system.
