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The subject of 4NF, but not 5NF, relation is introduced in the textbooks, but no theoretical study is achieved on their decomposition algorithm. In this kind of normal relation, there exists a special semantic constraint so called "cyclic nature constraint" which needs yet a theoretical analysis. On the other hand, in the practice of database design it is sometimes necessary to decompose a relation into two or more relations.
In this paper, we f11st mention the reason for decomposing a relation, and then give a rigorous defmition of cyclically constraint relation. Then by providing five Lemmas and their proofs, we describe in detail the characteristics of this kind of relation. We also introduce tow theorems and their proofs and provide the algorithms, based on these theorems to decompose the cyclically constrained relation, with a very high degree of flexibility. Finally, we discuss the results of this research.