  Let $\Omega$ and $\Omega_{\fin}$ be the sets of all interpolating Blaschke
products of type $G$ and of finite type $G$, respectively. Let $E$ and
$E_{\fin}$ be the Douglas algebras generated by $H^\infty$ together with the
complex conjugates of elements of $\Omega$ and $\Omega_{\fin}$, respectively.
We show that the set of all invertible inner functions in $E$ is the set of all
finite products of elements of $\Omega$ , which is also the closure of $\Omega$
among the Blaschke products. Consequently, finite convex combinations of finite
products of elements of $\Omega$ are dense in the closed unit ball of the
subalgebra of $H^\infty$ generated by $\Omega$. The same results hold when we
replace $\Omega$ by $\Omega_{\fin}$ and $E$ by $E_{\fin}$.
