The purpose of a good database logical design is to eliminate data redundancy and insertion, deletion and update abnomalies. For a temporal database, its normalization has been widely studied by using contraints of temporal functional dependency with multiple time granularities. Based on the process of normalization of traditional relational database, the concepts of temporal multivalued dependency (TMVD) with multiple time granularities based on temporal functional dependency and the theory of multivalued dependency of traditional relational databases are introduced. An axiomatization for TMVD is given. Because a finite set of TMVDs usually implies an infinite number of TMVDs, the notion of the temporal fourth normal form is introduced, and an axiomation for a finite closure to effectively capture a finite set of implied TMVDs is given, which are essential to the logical design. Temporal fourth normal form with respect to TMVDs is given, decomposition algorithm is presented that gives lossless T4NF decompositions, and the complexion of the algorithm is analyzed. In the meanwhile, the proof of the correctness and termination of the algorithm is given.