In recent papers [8], it has been pointed out that two invariant lists of integers, the ‘infinite zero orders’ and the ‘essential orders’ play a key role in the solution of the so called ‘Morgan's problem’, i.e. the row by row decoupling problem. The purpose of the present paper is to define the ‘block essential orders’ of a linear system with respect to the block decoupling problem. This is done through a new dynamic solution to the latter, based upon a procedure which extends to the block case, that previously given in [15] for Morgan's problem. This procedure is minimal in the sense that it leads to the least infinite zero structure for any decoupled system reachable from the original one.