Let \(\beta >0\), \(\alpha \beta >1+2\beta\), and consider a polynomial \(z^ 3+\alpha z^ 2-z+\beta\). It is shown that its maximum modulus M(r) is taken on some path from 0 to -1 and then from \(+1\) to \(\infty\), i.e. there is a jump for \(r=1\). In the last formula 2r should be 4r.