If the problem of human nature in psychological and social sciences has got indeed the character of paradigm, it should be openly admitted and solved, however difficult it might be. The most widely spread paradigm is that of egoism. Selfishness is ascribed to man (explicitly or implicitly) as a substantial (if not the only one) final determinant of his/her mentality. What kind of help can we expect from the new scientific discipline - evolutionary psychology? Evolutionary psychology asks what was the mental outfit of primary man that enabled him to solve problems in his/her original environment; i.e., in the environment to which he/she was adapted in the evolutionary process. And, further on, how does the original, evolutionarily stabilized mental outfit of man make itself useful in the present, fairly different environment? Altruism (between relatives and above all the reciprocal one) is a theme to which evolutionary psychologists pay great attention. The rise of the reciprocal altruism as an evolutionary stabilized strategy is conditioned by systematic, consistent and repeated exchange of roles ''giver'' and ''receiver''. The reciprocity of utility in the evolutionary process is controlled by the individual's reproductional success. The ultimate cause of the reciprocal altruism has got, therefore, the unambiguous character of individualism. On the other hand, the proximal mechanisms (motivation, emotions, feelings) arisen in the evolutionary process of the reciprocal altruism, as well as by them generated behaviour have got an unambiguous orientation at other individuals, and that positively - in the form of help or even self-sacrifice (devotion), cooperation. The development of the reciprocal altruism took place in Hominids several million years before the emergency of articulated speech. The enlarging brain of Hominids was - most probably - the result of natural selection of individuals, more capable to realize the reciprocal altruism with a long time range, with a large individual differentiation, with refined proportions of interchangeability, and to defend it against the ''cheaters''. As a further evolutionary step, the emergency of the oughtness dimension, the basic stone of human gift of morality, is considered. Face to face with the puzzle character of social intricacy, a successful individual was that one, who had got ''inbuilt'' well-tried cluse of what to do. The morality, in fact, functions - being effective just because of the fact that it has got an additive dimension of oughtness that enables to overcome - in actual situation - the barrier of egoistic desires, to disengage from them, and to help the others.