The aim of this note is to show that a linear system (

) is block-decouplable by means of static state feedback laws (

) with

invertible if and only if the infinite structure of (

) equals the union of the infinite structures of the subsystems (

) extracted from the given output partition. This result generalizes the ones recently obtained for Morgan\´s problem [6] and for the particular cases of right-invertible [7] or left-invertibie [8] systems.