  Let $D$ be a space of $2\times n$ matrices. Then the face of the cone of all
completely positive maps from $M_2$ into $M_n$ given by $D$ is an exposed face
of the bigger cone of all decomposable positive linear maps if and only if the
set of all rank one matrices in $D$ forms a subspace of $D$ together with zero
and $D^\perp$ is spanned by rank one matrices.
