Summary: This paper is based on the splitting operation for binary matroids that was introduced by T. T. Raghunathan et al. [Discrete Math. 184, No. 1–3, 267–271 (1998; Zbl 0955.05022)] as a natural generalization of the corresponding operation in graphs. In this paper, we consider the problem of determining precisely which cographic matroids \(M\) have the property that the splitting operation, by every pair of elements, on \(M\) yields a cographic matroid. This problem is solved by proving that there are exactly five minor-minimal matroids that do not have this property.