Following the US attack to Iraq on 20 of March, 2003, and the collapse of Baas regime, the Iraq political structure has been revolutionized, and a new political structure emerged. The major players of the new structure were Shiat, Kurds, and Soni groups. Social gaps were the major criterion for such classification. The first gap is the ethnic one dividing Iraq to to two Kurd and Arab communities. The second gap is the religeous gap causing two communities of Shiat and Soni to be formed. Accordingly, the Iraq's society has been divided into three nearly distinct and divisible parts of Shiat, Soni, and Kurd. Taking the ethnic-religous clashes and gaps in the existing Iraq society into consideration, some socio-political thinkers believe that the solution to this problem would be the Federalism political structure. Despite the fact that there were some opponents to this view, the suggestion was incorporated into the Iraq constitution. The major purpose of the present paper is to investigate the power triangualation in new Iraq based on the Federalism system. Thus, considering the nature and type of the issue, use was made of discriptive-analytic method and the library sort of collecting information was utilized to collect the required data.