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Let M and N be internally 4-connected binary matroids such that M has aproper N-minor, and |E(N)| is at least seven. As part of our project to developa splitter theorem for internally 4-connected binary matroids, we prove thefollowing result: if M\e has no N-minor whenever e is in a triangle of M, andM/e has no N-minor whenever e is in a triad of M, then M has a minor, M', suchthat M' is internally 4-connected with an N-minor, and 0 < |E(M)|-|E(M')| < 3.

Towards a splitter theorem for internally 4-connected binary matroids II