  For an oriented matroid M, and given a generic single element extension and a
generic single element lifting of M, the main result of [1] provides a
bijection between bases of M and certain reorientations of M induced by the
extension-lifting. This note is intended to somehow clarify and precise the
geometric setting for this paper in terms of oriented matroid arrangements and
oriented matroid programming, to describe and prove the main bijective result
in a short simple way, and to show how it consists of combining two direct
bijections and a central bijection, which is the same as a special case -
practically uniform - of the bounded case of the active bijection [5, 6]. (The
relation with the active bijection is addressed in [1] in an indirect and more
complicated way.)
