We consider the space $S$ of analytic functions bounded by 1 in modulus on the unit disk, endowed with the topology of locally uniform convergence. The set $B_d$ of Blaschke products of degree at most d is a compact subset of $S$. We will introduce a convenient system of coordinates for $B_d$ with the help of the Schur algorithm. In particular, we see that $B_d$ is homeomorphic to a ($2d+1$)-dimensional sphere.