Let \(\Gamma\) be a geometrically finite discrete group of isometries of real hyperbolic n-dimensional space \({\mathbb{H}}^ n\). We suppose that \(\Gamma\) is convex co-compact, contains no elliptic elements, and that the quotient \(M={\mathbb{H}}^ n/\Gamma\) has infinite hyperbolic volume. We study the Selberg zeta function introduced by Patterson for this class of groups and prove a trace formula refining and generalizing earlier results of Patterson. This trace formula connects the poles of the scattering operator to those of the meromorphically continued logarithmic derivative of the zeta function.