  We present a simple bijection between permutation matrices and descending
plane partitions without special parts. This bijection is already mentioned in
work of P. Lalonde (without giving the details); it involves the inversion
words of permutations and the (well-known) representation of descending plane
partitions as families of non--intersecting lattice paths. (Taking a short
detour, we will also exhibit how the (well--known) enumeration of descending
plane partitions follows easily from the evaluation of Andrew's determinant.)
