  Complete suppression of the heavy quarkonium due to the screening mechanism
of the quark-gluon plasma is proposed in the literature to be a signature of
the quark-gluon plasma detection at RHIC and LHC. However, since the heavy
quarkonium $\Upsilon$ production is experimentally measured in the Pb-Pb
collisions by the ALICE collaboration at LHC one has to study the $\Upsilon$
production from the quark-gluon plasma instead of studying the $\Upsilon$
suppression due to the screening mechanism of the quark-gluon plasma. In this
paper we derive the non-perturbative formula of the $\Upsilon$ production
amplitude from the quark-gluon plasma from the first principle in QCD which can
be calculated by using the lattice QCD method at the finite temperature.
