<p>The question of the relation between contractive conditions maybe extended to the problem of their iterates. It was shown by B. Fisher that fora Banach contraction there exists an iterate that fulfills Chatterjea contractivecondition, but the reverse relation holds under some restriction imposed on themetric space which assures that there exists an iterate of a Chatterjea contractionthat is a Banach contraction. However, the proposed restriction holds only for theidentity mapping which is not a Chatterjea contraction except for the singletondomain. We offer a possible adjustment of this approach with several examplesanswering some open questions on this topic.</p>