A note on binary matroid with no -minor

We prove that if M is an internally 4-connected binary matroid with an M ( K 5 ) -minor and with no M ( K 3 , 3 ) -minor, then either M has rank 4, or M is isomorphic to one of the following matroids: T 12 , T 12 / e , T 11 ˜ , T 12 ˜ , and T 13 ˜ .