  Let $G$ be a compact connected Lie group and let H be a subgroup fixed by an
involution. A classical result assures that the action of the complex reductive
group $H_C$ on the flag variety $F$ of $G$ admits a finite number of orbits. In
this article we propose a formula for the branching coefficients of the
symmetric pair $(G,H)$ that is parametrized by $H_C\backslash F$.
