Let consider a relation R=(A,B,C,D,E)
A primary key for the relation R is {B,C}
Functional dependency B ®E violates BCNF criteria. So relation R is decomposed into R1=(A,B,C,D) with functional dependency {A ®D} and R2=(B,E) with functional dependency {B®E}.
R2 is in BCNF.
We need to analyze R1. Candidate keys should be determined.
{A,B,C}+ = {A,B,C,D}
The only candidate key is A,B,C. The dependency A ®D is partial and violates BCNF conditions. It is necessary to decompose the relation R1 into R11=(A,B,C) and R12=(A,D).
The only candidate key for R11 is A,B,C, and it is a primary key. The only candidate key for R12 is A. Both relations satisfy BCNF criteria.
The decomposition of R into BCNF is
R11=(A,B,C), R12=(A,D), and R2=(B,E).