R. M. Miura, C. S. Gardner and M. D. Kruskal [J. Math. Phys. 9, 1204-1209 (1968; Zbl 0283.35019)] proved that solutions of the KdV equation \(u_ t=u_{xxx}+6uu_ x\) could be related to those of the equations \(w_ t=w_{xxx}+6ww_ z-(3/2)\epsilon^ 2w^ 2w_ x\) by means of the nonlinear transformation \(u=w-(1/2)\epsilon w_ x- (1/4)\epsilon^ 2w^ 2\). The similar transformations are called deformations, since they reduce to the identity transformation when \(\epsilon =0\). - B. A. Kupershmidt has given a construction of a deformation of any scalar Lax equation [Proc. R. Ir. Acad., Sect. A 83, 45-74 (1983)]. In the paper under review the author gives a construction of a deformation which is valid for isospectral flows of any matrix eigenvalue problem.