Necessary and sufficient conditions arc determined for the stabilization of an /-input, m-output, time invariant, linear and minimal system while block decoupling it by state feedback and a constant non-singular input transformation. The fixed poles of the block decoupled system are related to a subset of the transmission zeros of tho uncompensated system nnd a method is presented for assigning arbitrarily all the non-fixed poles of the compensated system. Finally, the observability of the block decoupled system is examined.