  The Chen-Fox-Lyndon theorem states that every finite word over a fixed
alphabet can be uniquely factorized as a lexicographically nonincreasing
sequence of Lyndon words. This theorem can be used to define the family of
Lyndon words in a recursive way. If the lexicographic order is reversed in this
definition, we obtain a new family of words, which are called the Nyldon words.
In this paper, we show that every finite word can be uniquely factorized into a
lexicographically nondecreasing sequence of Nyldon words. Otherwise stated,
Nyldon words form a complete factorization of the free monoid with respect to
the decreasing lexicographic order. Then we investigate this new family of
words. In particular, we show that Nyldon words form a right Lazard set.
