The subject of the present work is the sport arbitration at a global level, delimiting the field of study to the performance of the Court of Arbitration for Sport (CAS) as a decision-making body. The problem that led to the elaboration of this work was: how does the Court of Arbitration for Sport (CAS) form part of the decision-making body with juridical characteristics? Its main hypothesis is that the Court for Arbitration of Sport (CAS) is the highest instance of a non-state, but global, legal order whose decisions are competent not only for issues of purely sporting interest but also that set precedents for itself (which makes it selfreferential) and also concerns about issues pertaining to the fundamental rights of athletes and organizations. Main objective: to analyze, from basic notions of the Theory of Autopoietic Social Systems (such as complexity, transnationalization and autopoiesis) the Lex Sportiva and the Arbitral Court of Sport.Specific objectives: i) to observe Lex Sportiva, a non-state and transnational legal order arising from the regulation of the most varied professional sports; ii) to approach the CAS as the main center of juridicity in this multicentric order. Methodology: systemic-constructivist. Results: i) the emergence of Lex Sportiva in the hypercomplex, polyontextural and globalized society constitutes a true non-state legal order, whose autonomy, legitimacy and binding force are recognized by state orders; ii) its normative and decision-making processes deal with issues of high relevance not only to the sport itself but also to fundamental freedoms; iii) the CAS, in this context, reveals itself as a true non-state maximum court, whose decisions are fundamentally relevant to various aspects of the life of those involved in sports activities.