  In the framework of a newly developed factorization formalism which is based
on NRQCD, explicit cancellations are shown for the infrared divergences that
appeared in the previously calculated hadronic annihilation decay rates of
P-wave and D-wave heavy quarkonia. We extend them to a more general case that
to leading order in $v^2$ and next-to-leading order in $\alpha_s$, the infrared
divergences in the annihilation amplitudes of color-singlet
$Q\bar{Q}(^{2S+1}L_J)$ pair can be removed by including the contributions of
color-octet operators $Q\bar{Q}(^{2S+1}(L-1)_{J'})$,
$Q\bar{Q}(^{2S+1}(L-3)_{J''})$, ... in NRQCD. We also give the decay widths of
$^3D_J\rightarrow LH$ at leading order in $\alpha_s$.
