  The deletion order of a finitely generated Coxeter group W is a total order
on the elements which, as is proved, is a refinement of the Bruhat order. This
order is applied in [8] to construct Elnitsky tilings for any finite Coxeter
group. Employing the deletion order, a corresponding normal form of an element
w of W is defined which is shown to be the same as the normal form of w using
right to left lexicographic ordering. Further results on the deletion order are
obtained relating to the property of being Artinian and, when W is finite, its
interplay with the longest element of W.
