The aim of this paper is to discuss about the principle of the morality in the Brazilian Public Administration and the possibility to recognize it as a citizens' fundamental right specially with the development of the electronic government and the values of the future's constitutionalism which were purposed by Dromi. It presents the justification for this investigation, makes a review about the principle of administrative morality and its relation with the fundamental rights and then it explains how the values of the future's constitutionalism could be applied to the electronic government reality by recognizing the fundamental right of the good administration.