  The class of cographs or complement-reducible graphs is the class of graphs
that can be generated from $K_1$ using the operations of disjoint union and
complementation. By analogy, this paper introduces the class of binary
comatroids as the class of matroids that can be generated from the empty
matroid using the operations of direct sum and taking complements inside of
binary projective space. We show that a proper flat of a binary comatroid is a
binary comatroid. Our main result identifies those binary non-comatroids for
which every proper flat is a binary comatroid. The paper also proves the
corresponding results for ternary matroids.
