Stabilization of a linear, time-invariant system via stabilization of its main diagonal subsytems is the underlying problem in all diagonal dominance techniques for decentralized control. In these techniques as well as all Nyquist-based techniques, sufficient conditions are obtained under the assumption that the collection of the unstable poles of all diagonal subsystems is the same as the unstable poles of the overall system. We show that this assumption is by itself enough to construct a solution to the problem at least in cases where the diagonal subsystems have disjoint poles.