Abstract: The acyclic property of database data structure is an important property of the database theory and application. How to make an acyclic decomposition of the database schema is a relatively complex problem, and more complex is the α-acyclic decomposition problem when there exist inside conflicts in FD set F. Discussed in this paper is that when there exist generalized left-hand side conflicts or generalized right-hand side conflicts in FD set F which has inside conflicts, the relationship between the generalized left-hand side or generalized right-hand side conflicts and the symmetrical left-hand side attribute set, and the existing condition and property of the symmetrical left-hand side attribute set. The corresponding concepts, theorems and proof are also given. On this basis, a decision algorithm of the existence of generalized left-hand side or generalized right-hand side conflicts is presented. The correctness verification and algorithm analysis of the above mentioned algorithm are presented too.