In a recent paper we found an analytical formula for the constrained ordered weighted aggregation problem (OWA) when we need to maximize the objective function. In this note we prove that the method works in the case when we need to minimize the objective function. If in the case of the maximization problem we need to rearrange the coefficients in the constrained in nondecreasing order, for the nontrivial minimization problem, it suffice to rearrange them in nonincreasing order.