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A formal definition for the semantics of the Whole-Part relationship in the Unified Modeling Language or UML is introduced. This provides a fully directly usable specification which can be incorporated into version 2.0 of UML. An improvement to the current metamodel fragment relating to relationships is proposed, supplemented by the introduction of axioms expressed in the Object Constraint Language or OCL. The overall formalization relates to a clear and concise emphasis on carefully enunciated (primary) characteristics that apply to all instances of a new Whole-Part metatype. Specific kinds of the Whole-Part relationship are defined in terms of secondary characteristics, which must be possessed by subtypes: In UML 1.4, these are Aggregation (a.k.a. white diamond) and Composition (a.k.a. black diamond). Primary and secondary characteristics may then be consistently combined with each other. Consequently, this allows the possible introduction of supplementary forms of Whole-Part. Such a revision is necessary since Aggregation and Composition in UML 1.4 do not cover the full spectrum of Whole-Part theory.