Modern anti-discrimination law, with half a century of history, has its lights and its shadows. This work starts from the last ones, i.e., from its limits, and to solve them it is proposed to look at both the law and discrimination from a counter-hegemonic view. With this aim, the work is structured in three fundamental sections: in the first one it is framed the characterization of the law within what are often called "critical theories"; in the second one the concept of discrimination is inserted into the systemic theories of power; and in the third one the foundation for a new paradigm of antidiscrimination law based on the concept of subordiscrimination is laid. The use of this last concept will be precisely what will give name to the new model of antidiscrimination law that, consequently, will be renamed anti-subordiscrimination law.