Matchmaking is an important aspect of Web Services interactions. In a dynamic environment such as the Internet, matchmaking services require rich and flexible metadata as well as efficient matching algorithms. The Semantic Web technologies, especially OWL and OWL-S, are gaining momentum and generating suitable technologies and tools to cover both the metadata and the algorithmic aspects. In this paper, we introduce a step-by-step matching algorithm that can be used to determine the semantic similarity of two Web Services. The matching algorithm is based on the Description Logics reasoning services and operates on service descriptions in OWL and OWL-S, with the matching results ranked. The algorithm is implemented in a prototype system, based on the well-known Racer description logics system.