Remote-component-based software systems (CBS) must provide high maintainability to support operation over long periods of time and correspond to changes in enterprise requirements/environments. Measurements of the degree of complexity of a system are one technique for evaluating maintainability. However, conventional complexity metrics are unable to reflect the overall complexity of the system, because they do not incorporate a procedure to account for characteristics of CBS. To help maintenance work proceed smoothly, we propose a new metric that measures the coupling-based complexity of CBS by abstracting the target system's structure through a step-wise process and taking into consideration the characteristics of remote components. Our metric can be applied to CBS based on the Enterprise JavaBeans component architecture. As a result of experimental evaluations, it is found that our metric better reflects the maintainability than conventional metrics. It is also found that our metric is nonredundant with existing metrics such as Coupling Factor.