  Let $U$ be a multiply connected domain of the Riemann sphere $\hat{C}$ whose
complement $\hat{C}\setminus U$ has $N<\infty$ components. We show that every
conformal map on $U$ can be written as a composition of $N$ maps conformal on
simply connected domains. This improves on a recent result of D.E. Marshall,
but our proof uses different ideas, and involves the uniformisation theorem for
Riemann surfaces.
