This thesis is about the importance to justify decisions in the paradigm that actually is being drawned in Law. This is a moment of democratic opening and judicial decisions transparence, so the reasoning in which they are foundated, are essential to legitimate them and to guarantee the society acceptance. Towards this new Law´s approach, Robert Alexy proposes a non positivist theory, in which, Law in order to be legitim, besides positivated, needs to be correct, connected to a claim to correcteness. This work presents, in a panoramic way, Robert Alexy´s theory, focusing how the author articulates morality and Law and how he elaborates one of the most nowadays sofisticaded law´s application procedure. But then arises an important issue: is this new procedure capable to reach fairness decisions? The theory of legal reasoning, in the way it is actually presented, does not seems enough. We understand that the claim to correcteness must explicitely be included in the theory of legal reasoning, by the form of a third step, the correcteness criteria. So it will enables better efficacy in reaching correct judicial decicions. After a presentation of an Alexy´s proposal to define this correcteness criteria, it is being done some little incursions on Jürgen Habermas, Klaus Günther e Ronald Dworkin, in order to find contributions to help elaborating this criteria.