Moral maxims are supposed to be universal, but in what sense is their universality acceptable? The universality of morality is facing two challenges: 1.Are there any moral maxims applicable at all time and place? 2. Even if a morality free from spacio-temporal restrictions can be discovered, is such an universal morality desirable? Bauman gives these two questions a negative answer from a post-modern point of view. He claims that each moral judgement is unique, every moral agent is irreplaceable, and the relationship between one person and another is asymmetrical, therefore, it is not appropriate to ask all people to bear the same responsibility. Seeking for moral universality is a dream of modern philosophers, he indicates, and should be debunked by postmodernists. In this respects, we--whether as moral philosophers or moral educators--are trapped by a dilemma: we uphold reciprocity (e.g. mutual respect) which is understood as a manifestation ofuniversality on the one hand, and on the other we insist on moral subjectivity so that moral maxims whould not become egalitiarian commands. In this paper, I try to review the concept of "universality" and furthermore, distinguish different levels of morality. By so doing, I wish the dilemma in question can be resolved and the varied emphases of moral education on various levels can be shown.