  Let X be the direct product of two Grassmann varieties of k- and l-planes in
a finite-dimensional vector space V, and let B be the isotropy group of a
complete flag in V. We consider B-orbits in X, which are an analog to Schubert
cells in Grassmannians. We describe this set of orbits combinatorially and
construct desingularizations for the closures of these orbits, similar to the
Bott--Samelson desingularizations for Schubert varieties.
