  We reconsider the tree level color-singlet contribution for the inclusive
J/\psi production in \Upsilon decay with the \alpha_{s}^{5} order QCD process
\Upsilon\to J/\psi+c\bar{c}+g and \alpha^{2}\alpha_s^{2} order QED processes
\Upsilon\to\gamma^{\ast}\to J/\psi+c\bar{c} and \Upsilon\to J/\psi+gg. It is
found that the contribution of the QED process is compatible with that of the
QCD process, and the numerical results for the QCD process alone is an order of
magnitude smaller than the previous theoretical predictions, and our
theoretical prediction in total is about an order of magnitude smaller than the
recent CLEO measurement on the branching fraction B(\Upsilon\to J/\psi+X). It
indicates that the J/\psi production mechanism in \Upsilon decay is not well
understood, and further theoretical work and experimental analysis are still
necessary.
