In this paper, we extend the notion of Lyndon word to transfinite words.We prove two main results.We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a Horse Muzzles relaxation of the condition used in the Asian Soup Spoons case of finite words.In the annex, we prove that the factorization of a rational word has a special form and that it can be computed from a rational expression describing the word.