  We present a different proof of the characterization of non--degenerate
recurrence sequences, which are also divisibility sequences, given by Van der
Poorten, Bezevin, and Petho in their paper "A Full Characterisation of
Divisibility Sequence". Our proof is based on an interesting determinant
identity related to impulse sequences, arising from the evaluation of a
generalized Vandermonde determinant. As a consequence of this new proof we can
find a more precise form for the resultant sequence presented in their paper,
in the general case of non--degenerate divisibility sequences having minimal
polynomial with multiple roots.
