  A previous counterexample to disprove k_T-factorization for H_1+H_2 -->
H_3+H_4+X is extended calculationally to one higher order in gluon exchange.
The result is that, by explicit calculation, standard k_T-factorization fails
for the unpolarized cross-section for the production of hadrons of high
transverse momentum in hadron-hadron collisions.
