This article has as main objective to point a way to solve the conflicts between the fundamental rights or constitutional principles, more specifically the conflict between the protection of the immaterial cultural manifestation of African matrix religion that uses animals sacrifice and the environment protection ecologically balanced with emphasis in the fauna protection. The fundamental rights are studied in their theoretical genesis and legislative evolution up to the present perspective of the constitutional treatment of the subject. In the end it is offered a technique which intends to restricts the principles and makes possible the permanence and realization of both, guaranteeing the constitutional effectiveness.