  We obtain a multiplication formula for cluster characters on (stably)
2-Calabi-Yau (Frobenius or) triangulated categories. This formula generalizes
those known for arbitrary pairs of objects and for Auslander-Reiten triangles.
As an application, we show that for cluster algebras of acyclic types,
specialization of a cluster variable to 1 sends all cluster variables to
elements of a cluster algebra of smaller rank. We also obtain application to
the reduction of friezes of acyclic type.
