We introduce the notion of weak reduciblity for Dupin
submanifolds with arbitrary codimension. We give a complete
characterization of all weakly reducible Dupin submanifolds,
as a consequence of a general result on a broader class of
Euclidean submanifolds. As a main application, we derive an
explicit recursive procedure to generate all holonomic Dupin
submanifolds in terms of solutions of completely integrable
systems of linear partial differential equations of first
order. We obtain several additional results on Dupin
submanifolds.