Let \(E\) be a non-trivial extension of the maximal ideal of a point \(P\) on \({\mathbb P}^2\) by \({\mathcal O} _{{\mathbb P}^2} (1)\). Then \(E\) is a vector bundle on \({\mathbb P}^2\) and obviously the Harder–Narasimhan filtrations of Frobenius pull backs of \(E\) never split. Clearly, there are many other examples that can be obtained in this way. One can also blow-up the point \(P\) so that the quotients in the Harder–Narasimhan filtration are locally free. The paper under review contains a more complicated example showing that the Harder–Narasimhan filtrations of Frobenius pull backs need not split.