When the simultaneous disturbance rejection and regular block decoupling problem by static state feedback is solvable, and under some unrestrictive minimality assumption, all the poles of the closed-loop system can be placed, except the so-called fixed poles (which are present for any solution). We present here a geometric characterization for this set of fixed poles as well as a constructive procedure (based on geometric tools) for designing a feedback solution of the problem which assigns the remaining poles to arbitrary prespecified locations.