A new similarity block transformation is derived to transform state equations of multi-input-multi-output (MIMO) systems in general coordinates to those of cascade or parallel block canonical forms so that irreducible divisors of the characteristic A-matrix can be determined. Using the obtained complete set of irreducible divisors of the A-matrix, an extended block partial fraction expansion of the matrix fraction description of a MIMO system is developed. Applications of the developed results to the model reduction and the suboptimal block controller design for high order systems are illustrated.