Prior research attempts to formalize the structure of object-oriented design patterns for a more precise specification of design patterns. It also allows automation support to be developed for user-defined design patterns in the future CASE tools. Targeting to a particular type of automation (e.g. verification of pattern instances), previous specification approaches over-specify pattern structures to a certain extend. Over-specification makes pattern specification ambiguous and disallows the specification language to be used for specifying compound patterns. In this paper, we present the structural properties of design patterns which reveal the tract nature of pattern structures. To support these properties so as to solve the over-specification