A system (A,Bd) with two input channels which correspond to its two interconnected subsystems (A11,B22) and (A22,B22), is considered. The conditions for (A,Bd) to be controllable by only one of the input channels are then formulated. The conditions found replace the usual controllability conditions and involve only certain submatrices of the initial system matricesAandBd; as such, they are particularly well suited for the analysis of large-scale systems.