The Mexican Constitution establishes the obligation to found and motivate every act of authority, including judicial decisions. This obligation has been a vital protection to people s right and liberties in Mexico against illegal acts from the authorities. Unfortunately, the New York Convention does not obligate arbitrators to reason the awards. This situation may generate a conflict of law within the Mexican legal system, that is, between the Constitution and the application of the New York Convention. The Constitution is unanimously considered by the Mexican doctrine and, more importantly, by the Mexican Supreme Court of Justice, as the Supreme Law. The amparo suit, or constitutional injunction suit, is a specific legal figure created to impede or to bar any act or law considered unconstitutional. The issue is whether federal courts in Mexico can properly set aside an award through an amparo suit, although acting in accordance with the international legal system especially without breaching Mexico s obligation under the VCLT. Considering that the article V(II)(b) of the New York Convention may provide with the public policy exception a way out.