That was not an accident.

That was no accident.

no=not a 或 not any

no用在名词前叫名词否定。以上两句的意思是一样的。但一般认为名词否定句的语气要强烈一些，多用于书面语。

They are not staying with us any longer.

They are no longer staying with us.

no longer=not...any longer. 第一句any longer位于句末，似乎更为强调“不再”的意味。