We introduce a novel algebraic composition law that transforms the interval \((-1,1)\) into a commutative group, uncovering unique structural insights. Leveraging this group structure, we construct a two-sided Blaschke product and investigate its analytical properties. The main result demonstrates the existence of a surjective composition operator on the model space associated with this Blaschke product. This approach not only clarifies the underlying algebraic framework but also addresses gaps in previous work, offering a more transparent proof and expanding on the established theory.
