  We answer in the affirmative the following question raised by H. H. Corson in
1961: "Is it possible to cover every Banach space X by bounded convex sets with
nonempty interior in such a way that no point of X belongs to infinitely many
of them?" Actually we show the way to produce in every Banach space X a bounded
convex tiling of order 2, i.e. a covering of X by bounded convex closed sets
with nonempty interior (tiles) such that the interiors are pairwise disjoint
and no point of X belongs to more than two tiles.
