Given an ordered alphabet anda permutation, according to the lexicographic order,on the set of suffixes of a word w,we present in this article a linear time and space method to determine whether a word w' has the same permutation on its suffixes.Using this method, we are then also able to build the class of all thewords having the same permutation on their suffixes, first of all the smallest one.Finally, we note that this work can lead to a method for generating a Lyndon word randomly in linear time or for computingthe set of Lyndon words of length n.