Abstract: The purpose of a good database logical design is to eliminate data redundancy and insertion, deletion and update anomalies. Temporal database is the same case. In this paper, the notions of temporal elementary functional dependency, temporal elementary key, temporal simple key are introduced. On this basis, the normalization of temporal database is studied by using constraints of temporal functional dependency(TFD) with multiple time granularities; the concept of temporal elementary key normal form(TEKNF) and temporal simple normal form(TSNF) is introduced; the proof that the normalization degree of both normal form is between T3NF and TBCNF and the normalization degree of TEKNF is lower than that of TSNF is given. Decomposition algorithms that give lossless, dependencypreserving, TEKNF decompositions and lossless, dependencypreserving, TSNF decompositions and the proof for its termination and correction are also given.