Component Based System (CBS) development is about assembling individual components to produce a working system. However, its overall complexity does not only depend on the complexity of individual components. Further, component source code information is usually unavailable and they introduce additional properties such as constraints associated with its use, interactions among components, and customizability. The traditional complexity metrics are not adequate and do not easily apply to CBS as they mainly focus on either Lines of Codes (LOC) or information based on objects, classes and their inheritance properties. Recent CBS research suggests that most faults are found in few components. A complexity measure at specification level can be used for identifying these components; and precautionary actions can be taken to avoid the likely failures and to lower maintenance costs. There is therefore a need to develop a new technique for measuring the complexity of a component specification. This paper describes a complexity measure for a component specification written in Unified Modeling Language (UML).