A new canonical form for the action of restricted system equivalence on controllable singular systems is given. The construction of this form is based on the Weierstrass decomposition of the singular system into a slow and a fast subsystem. Both subsystems are transformed into Hermite canonical form. The resulting Hermite canonical form for singular systems has a particularly simple structure and is expected to be useful for e.g. identification purposes. Continuity properties of the Hermite form are investigated and the nonexistence of a globally defined continuous canonical form for controllable singular systems is shown.