  Let $G=G_{n}=GL(n)$ be the $n\times n$ complex general linear group and embed
$G_{n-1}=GL(n-1)$ in the top left hand corner of $G$. The standard Borel
subgroup of upper triangular matrices $B_{n-1}$ of $G_{n-1}$ acts on the flag
variety of $G$ with finitely many orbits. In this paper, we show that each
$B_{n-1}$-orbit is the intersection of orbits of two Borel subgroups of $G$
acting on the flag variety of $G$. This allows us to give a new combinatorial
description of the $B_{n-1}$-orbits by associating to each orbit a pair of Weyl
group elements. The closure relations for the $B_{n-1}$-orbits can then be
understood in terms of the Bruhat order on the Weyl group, and the
Richardson-Springer monoid action on the orbits can be understood in terms of
the classical monoid action of the Weyl group on itself. This approach makes
the closure relation more transparent than in earlier work of Magyar and the
monoid action significantly more computable than in our earlier papers, and
also allows us to obtain new information about the orbits including a simple
formula for the dimension of an orbit.
