It is always possible to decompose a relation into a set of relations that are in BCNF such that:

It is always possible to decompose a relation into a set of relations that are in 3NF such that:

BCNF3NF
RedundancyLess than 3NFMore than BCNF
Lossless DecompositionAlways guaranteedAlways guaranteed
Dependency PreservationNot guaranteedAlways guaranteed