Sometimes we also use the negative form to ask a question with a certain meaning:

--Shouldn't he take an asprin? (meaning he should take an asprin but he isn't)

--Yes thats what the doctor said he should do.

In this case never separate "not" from "should" do not say or write

:"Should he not take an asprin?"

Should and shouldn't

We use subject+ should + verb to say something is a good ideas.
We use subject+ shouldn't + verb to say something is not a good ideas.