Web Service composition has become indispensable as a single web service cannot satisfy complex functional requirements. Composition of services has received much interest to support business-to-business (B2B) or enterprise application integration. An important component of the service composition is the discovery of relevant services. In Semantic Web Services (SWS), service discovery is generally achieved by using service profile of Ontology Web Languages for Services (OWL-S). The profile of the service is a derived and concise description but not a functional part of the service. The information contained in the service profile is sufficient for atomic service discovery, but it is not sufficient for the discovery of composite semantic web services (CSWS). The purpose of this article is two-fold: first to prove that the process model is a better choice than the service profile for service discovery. Second, to facilitate the composition of inter-organisational CSWS by proposing a new composition method which uses process ontology. The proposed service composition approach uses an algorithm which performs a fine grained match at the level of atomic process rather than at the level of the entire service in a composite semantic web service. Many works carried out in this area have proposed solutions only for the composition of atomic services and this article proposes a solution for the composition of composite semantic web services.