Linear computation of unbordered conjugate on unordered alphabet

We present an algorithm that, given a word w of length n   on an unordered alphabet, computes one of its unbordered conjugates. If such a conjugate does not exist, the algorithm computes one of its conjugates that is a power of an unbordered word. The time complexity of the algorithm is O(n)O(n): the number of comparisons between letters of w is bounded by 4n.