Internally 4-connected binary matroids with cyclically sequential orderings

We characterize all internally 4-connected binary matroids M with the property that the ground set of M can be ordered (e"0,...,e"n"-"1) in such a way that {e"i,...,e"i"+"t} is 4-separating for all [email protected]?i,[email protected]?n-1 (all subscripts are read modulo n). We prove that in this case either [email protected]?7 or, up to duality, M is isomorphic to the polygon matroid of a cubic or quartic planar ladder, the polygon matroid of a cubic or quartic Mobius ladder, a particular single-element extension of a wheel, or a particular single-element extension of the bond matroid of a cubic ladder.