  Let $\A$ be a finite non-empty set and $\preceq $ a total order on $\A^\nats$
verifying the following lexicographic like condition: For each $n\in \nats$ and
$u, v\in \A^n,$ if $u^\omega \prec v^\omega$ then $ux\prec vy$ for all $x, y
\in \A^\nats.$ A word $x\in \A^\nats$ is called $\omega$-Lyndon if $x\prec y$
for each proper suffix $y$ of $x.$ A finite word $w\in \A^+$ is called
$\omega$-Lyndon if $w^\omega \prec v^\omega$ for each proper suffix $v$ of $w.$
In this note we prove that every infinite word may be written uniquely as a
non-increasing product of $\omega$-Lyndon words.
