I have found in several books the following affirmation :
Let $f: \Delta \rightarrow \Delta$ be a non constant holomorphic function that extends continuously to $\overline{\Delta}$, $\Delta$ being the open unit disk. Then $f$ is a finite Blaschke product, i.e. of the form $B(z) = e^{i \theta} \prod_{k=1}^d \frac{z- a_i}{1-\overline{a_i} z}$
Now it is not hard to check that those rational fractions do indeed send $\Delta$ onto $\Delta$, but I do not know where to find a proof that they are the only ones.
Where can I find that proof in the literature ? I am not interested in the infinite product case, only finite. (Of course, if anyone is kind enough to post a proof, that would do fine as well =)