Let Ω be the set of all interpolating Blaschke products unimodular on the trivial Gleason parts ofM(H∞. Let Ωfi:be the subset of Ω consisting of elements having finitely many roots in each part except the open unit disk. SupposeE(resp.Efiis the Douglas algebra generated byH∞and the complex conjugates of elements of Ω (resp. Ωfi). Our main results are that the set of all invertible inner functions in Ω (resp. Ωfi). is the set of all finite products of elements of Ω (resp. Ωfi), which is also the closure of Ω (resp. Ωfi) among the Blaschke products. Consequently, finite convex combinations of finite products of elements of Ω (resp. Ωfi).are dense in the closed unit ball of the subalgebra ofH∞generated by Ω (resp. Ωfi).