  Let $\mathcal{C}$ be a Hom-finite triangulated 2-Calabi-Yau category with a
cluster tilting object. Under some constructibility assumptions on
$\mathcal{C}$ which are satisfied for instance by cluster categories, by
generalized cluster categories and by stable categories of modules over a
preprojective algebra, we prove a multiplication formula for the cluster
character associated with any cluster tilting object. This formula generalizes
those obtained by Caldero-Keller for representation finite path algebras and by
Xiao-Xu for finite-dimensional path algebras. It is analogous to a formula
obtained by Geiss-Leclerc-Schr\"oer in the context of preprojective algebras.
