Multidimensional databases in data warehousing and OLAP areas are emerging as dominant approach with decision support applications. This paper discusses a multidimensional database model to use such as hierarchical relationships and more complex relationships expressed by functional dependencies for constructing databases and processing queries. The influences of functional dependencies to multidimensional spaces are inspected formally and a multidimensional database model is proposed, which consists of a multidimensional space and a set of relations. A design method of multidimensional databases utilizing functional dependencies is given for the model. It is also shown how the basic operations, projection, selection, and aggregation are processed in the proposed model.