Nietzsche's worldview is a little topsy-turvy, and we should bear that in mind. For Nietzsche, 'conventional' morality — the kind of thing taught in churches, inscribed in law, learned at our parent's knee, or otherwise authoritatively delivered from on high — is almost entirely bankrupt. The people who convey it are not interested in morality, only in power and social control; the people who are obedient to it are merely concerned with the appearance of virtue and respectability, and don't give a thought to the substance of it. It's the height of hypocrisy: adhering to the letter of moral stricture while completely abandoning the spirit of it.
Nietzsche's übermensch, thus, wants to transcend 'conventional' morality to achieve a deeper and more thorough sense of morality. Unfortunately, the distinction between transcending conventional morality and discarding morality entirely is difficult to convey. The übermensch is never immoral, even when violating conventional morality directly, because s'he is responding to the essence of the moral spirit. The übermensch is never nihilistic. In fact, Nietzsche associates nihilism with the worst of those espousing conventional morality: the ones who speak 'moral' words with no interest in or understanding of their essence. But it is all too easy for someone to fall into nihilism while thinking one is following the path of the übermensch. Rejecting conventional morality is necessary, but not sufficient; transcending morality demands a level of philosophical insight that most people do not grasp.