We shortly recall the O(n3 + out) algorithm from [9]. In this algorithm, it has been shown that each maximal clique is uniquely described by the 3 parameters t, h and v denoting the hypotenuse t of the lowest semi-square, the highest base h of any semi-square and the rightmost vertical side v. The drawback of the algorithm given in [9] is that it needs O(n3) time even if there are only very few maximal cliques. In the case of c-max-tolerance graphs we can now present a considerably improved output-sensitive algorithm.