A problem of P. Seymour on nonbinary matroids

The following statement fork=1, 2, 3 has been proved by Tutte [4], Bixby [1] and Seymour [3] respectively: IfM is ak-connected non-binary matroid andX a set ofk-1 elements ofM, thenX is contained in someU42 minor ofM. Seymour [3] asks whether this statement remains true fork=4; the purpose of this note is to show that it does not and to suggest some possible alternatives.