  Within the nonrelativistic QCD (NRQCD) factorization framework, we calculate
the exclusive decay process \eta_b \to J/\psi J/\psi to next-to-leading order
in the strong coupling constant, while at leading order in charm quark relative
velocity. It is found that this new contribution to the amplitude is comparable
in magnitude with the previously calculated relativistic correction piece, but
differs by a phase about 90^\circ. Including this new contribution will
increase the previous prediction to B(\eta_b \to J/\psi J/\psi) substantially,
thus brightening the discovery potential of this clean hadronic decay channel
of \eta_b in the forthcoming LHC experiment.
