A primitive word is a Lyndon word if is minimal among all its conjugates with respect to some lexicographic order. A word is bordered if there is a nonempty word u such that for some word . A right extension of a word of length n is a word wu where all factors longer than n are bordered. A right extension wu of is called trivial if there exists a positive integer k such that for some word .
We prove that Lyndon words have only trivial right extensions. Moreover, we give a conjecture which characterizes a property of every word which has a nontrivial right extension of length .