Decentralized integral control is one of the most popular control strategies used in practice. An important issue associated with this strategy is the analysis of Decentralized Integral Controllability (DIC). Campo and Morari showed that for a given process, if its steady state gain matrix is not critically D-stable, its DIC can be determined by using its steady state gain matrix. This technical note investigates decentralized integral control with a special focus on the DIC analysis of processes whose steady state gain matrices are critically D-stable. First, we introduce a new unconditional stability criterion. Then, by using the proposed criterion, it is proved that for up to four-channel processes, their DIC can be totally determined by their steady state gain matrices. We also present a multi-loop PI control design method, which provides an explicit lower bound of the proportional coefficient to achieve decentralized unconditional stability for low dimensional processes. For higher dimensional processes, this technical note presents a six-channel process whose DIC property cannot be determined only by its steady state gain matrix, contradicting the view of some other researchers.