Finite Blaschke Products and Decomposition

Let $B(z)$ be a finite Blaschke product of degree $n$. We consider the problem when a finite Blaschke product can be written as a composition of two nontrivial Blaschke products of lower degree related to the condition $% B\circ M=B$where$M$ is a M"{o}bius transformation from the unit disk onto itself.