Constitutions are social and historical artefacts that take part in the government of humans. Based on a comparison of how contemporary ‘global’ and historical ‘local’ constitutional documents establish power relations between ‘humans’ and their ‘government’, this article suggests that both types of documents involve different constitutive logics. Global constitutional documents create a ‘new normativity’ – a reversed constitution – that turns the historical relationship between pouvoir constituant and pouvoir constitué on its head. Such documents shift the primary responsibility for human rights from governments to humans. Research in the academic field of global constitutionalism omits this constitutional reconfiguration. By offering a more historically sensitive and reflexive account of constitutionalization, the field of global constitutionalism can realize an as yet unexplored critical potential.