Can we get HIV AIDS if I am having sex WITHOUT any protection & I KNOW that NONE of us is HIV positive?

HIV is virus infection. It should mean HIV cannot spread unless the Virus IS present, during the sexual intercourse. So, if i verify, before having sex for the first time, that my partner and I have no infectious STD, Will it be safe to do it without ANY protection at all? I know my partner and me are both totally faithful to each other...