Nowadays the need to create (or construct) new ethical norms emerges constantly in the spheres of politics, medicine, ecology, demography etc. But can we call normative ethics (i. e. ethics which not only describes and explains facts of the society's moral life but also postulates certain moral norms and principles) a science? The majority of contemporary logicians will answer negatively. According to them normative ethics cannot be a science since it is impossible to give scientific (logically correct) proof of its judgments. This paper makes an attempt to offer a logically correct basis for moral norms. To achieve this goal, I'll use the methods proposed within the frameworks of intuitionistic and constructive mathematics of the XX century. The concept of feasibility should play in ethics the role similar to which of the concept of possibility of object's construction (constructability) in mathematics. The existence of a moral norm depends on its implementation: that is why feasibility should be viewed as a proof of a norm. Moreover, we should speak not only about our physical capacity to implement an action prescribed but also about its coherence (consistency) with already existing moral prescriptions. We should regard as unfeasible any norm whose implementation excludes implementation of a norm already well-established. Any moral code containing such a norm should be regarded as inconsistent. As a result of application of these methods a new constructive ethics will emerge, which could be employed in different spheres of the contemporary social life.