Normal form after decomposition of a relation

Question

I came across a text recently which claims that if we perform a lossless decomposition of a relation R into smaller relations R1 and R2, and if R is in 3NF, both R1 and R2 are 3NF.

I felt a bit suspicious regarding this claim, but couldn't find anything to prove this statement wrong.

Am I correct in thinking that this statement doesn't hold all the time, or Am I wrong? It would be really helpful if someone can correct me if I am wrong?

Thanks in advance!