Hashing a hash increases security?

Question

Well a colleague of mine has been insisting on the idea of hashing a hash, I think they use in the company where he works The hash is in md5. I’ll explain as an employee: When registering a new user in the database would be generated a hash of the informed password, but this hash would not be recorded in the bank yet, there would be a change of positions and after that this hash serveria as a basis to create another hash, and then yes, this other hash would be recorded in the bank. This increases system security or is just a waste of time?

There’s another question here on stack overflow, which talks about good patterns, I don’t want to know how to make a safe hash, I want to know if a hash hash would increase security! So this is not pointed out in the other text!