A solution is presented to a long-standing open problem of linear control theory, the block decoupling by static-state feedback. The problem was introduced in 1970 and all past solutions were obtained under restrictive assumptions on system, block structure, and decoupling feedback. The present formulation avoids any restrictive hypotheses. The key notion is that of the block interactor. The existence of decoupling feedback is conditioned by system invariants with respect to the permissible transformations. A block decoupling algorithm is presented, which permits to determine the sizes of the smallest diagonal blocks attainable.