  One characterization of binary matroids is that the symmetric difference of
every pair of intersecting circuits is a disjoint union of circuits. This paper
considers circuit-difference matroids, that is, those matroids in which the
symmetric difference of every pair of intersecting circuits is a single
circuit. Our main result shows that a connected regular matroid is
circuit-difference if and only if it contains no pair of skew circuits. Using a
result of Pfeil, this enables us to explicitly determine all regular
circuit-difference matroids. The class of circuit-difference matroids is not
closed under minors, but it is closed under series minors. We characterize the
infinitely many excluded series minors for the class.
