Bcnf decomposition proper procedure?

Question

R(ABCDE)

{A→BC, CD→E, B→D, E→A}

How to convert it into bcnf?

I hv seen 2-3 ways to convert into bcnf.

And i dont find it possible to convert into bcnf with dependency preserving.

Is there any proper procedure works for all cases?

Lossless join for a database in bcnf is tht joining of the decomposed table or relation will give complete relation set.

Plz someone explain it 

Answer 1

Follow any valid method but remember Dependency Preservation is not compulsorily required. Only thing compulsory is lossless join which you know.

Therefore,conversion to BCNF will not always be Dependency Preserving but we still go for it.

If you still want to Preserve the Dependency, we arbitrarily add the attribute whose dependency was lost. 

For example, say B > D was lost in BCNF, and say we have a relation(table) now which has A and D as the attributes, then we arbitrarily add B attribute to this relation(table). NOTE: This addition doesn't violates anything. This way now B>D is now applicable to this relation(table) and hence FD is preserved.