  We give the maximal distance between a copula and itself when the argument is
permuted for arbitrary dimension, generalizing a result for dimension two by
Nelsen (2007), Klement and Mesiar (2006). Furthermore, we establish a subset of
$[0,1]^d$ in which this bound might be attained. For each point in this subset
we present a copula and a permutation, for which the distance in this point is
maximal. In the process, we see that this subset depends on the dimension being
even or odd.
