  Saito gave a nice and efficient criterion to determine whether the module of
logarithmic derivation associated with a reduced divisor in a complex variety
is free or not. The aim of this note is to propose a new proof of this
criterion, in the affine space, in the projective space, and for
multiderivations, based on straightforward observations concerning free and
reflexive modules. This point of view also allows us to prove a generalized
version of the Saito criterion that applies to derivation modules associated
with several polynomials.
