The system considered is Ex=Ax + Bu, y= Cx, with E singular. It is shown that infinite decoupling zeros can be defined, and these induce a fourfold decomposition, of that part of the system giving rise to the polynomial port of the transfer function matrix, analogous to Kalman'B canonical decomposition. Minimal indices are also defined, and are shown to be equal to dynamical indices based on the work of Forney and studied recently by Rosenbrock and Hayton.