My biochemistry book says that beta-pleated sheets is a form of secondary structure of proteins, and it is formed between two or more polypeptide chains.
I wonder why the sentence in bold doesn't belong to the quaternary structure instead?!
Quarternary structure is between separate protein chains or proteins themselves. Beta sheets are a form of secondary structure which is within a single polypeptide.
Sure, some of the structures in quarternary complexes will be between “two or more peptide chains”, but the stipulation that these not be part of the same polypeptide chain would be necessary.