We describe a calculus that is specific to non-repudiation protocols. The calculus uses the correspondence assertion of Woo and Lam, that is, if there is a non-repudiation of receipt there should be a corresponding non-repudiation of origin. The calculus is a subset of the Pi calculus. The basic constructs are modified in order to handle properties of non-repudiation. We offer a formal syntax and an operational semantics of the calculus. We show the usefulness of the calculus by describing Zhou optimistic protocol.