Co-hyponormality of composition operators on the Hardy space

On the Hardy space of the disk, we derive a formula for the norm of a composition operator with linear fractional symbol acting on a reproducing kernel. With this norm formula, a necessary condition will be given for the hyponormality of the adjoint of a composition operator with linear fractional symbol when that symbol maps the unit disk into itself. This necessary condition is an improvement on a condition given by Sadraoui and partially answers a question raised by Cowen and MacCluer.