Is this relation in Boyce-Codd's Normal Form?
Assuming that each book has a different title, you are correct in thinking that the relation is not in BCNF.
In fact, the (only) candidate key of the relation is  Book_title, so the functional dependency User_id -&gt; User_name violates the definition of BCNF. Assuming that a cover of the dependencies are:
User_id -&gt; User_name    (each user_id identifies a user with a certain name)
Book_title -&gt; User_id   (each book can be borrowed only by a certain user)

a decomposition of the original relation in BCNF is:
R1(User_id, User_name)  with candidate key User_id
R2(Book_title, User_id) with candidate key Book_title