Data warehouses are a major component of data-driven decision support systems (DSS). They rely on multidimensional models. The latter provide decision makers with a business-oriented view to data, thereby easing data navigation and analysis via On-Line Analytical Processing (OLAP) tools. They also determine how the data are stored in the data warehouse for subsequent use, not only by OLAP tools, but also by other decision support tools. Data warehouse design is a complex task, which requires a systematic method. Few such methods have been proposed to date. This paper presents a UML-based data warehouse design method that spans the three design phases (conceptual, logical and physical). Our method comprises a set of metamodels used at each phase, as well as a set of transformations that can be semi-automated. Following our object orientation, we represent all the metamodels using UML, and illustrate the formal specification of the transformations based on OMG's Object Constraint Language (OCL). Throughout the paper, we illustrate the application of our method to a case study.