BCNF Decomposition is the problem of decomposing a relation schema into Boyce-Codd normal form (BCNF). A relation schema $R$ is in Boyce Codd Normal Form (abbr. BCNF) if for all non-trivial FDs $X \rightarrow Y$ in $F^+$, $X$ is a superkey. In extending this notion to database schemas, we must be conscious of the UR-assumption. We say that $R_i = <ATTR_i,F_i>$ is in BCNF if the schema $<ATTR_i, F^+[ATTR_i]>$ is in BCNF, and $D$ is in BCNF if each $R_i$ is.