DD(Decision Diagrams) is an efficient operational data structure for an optimal expression of boolean functions. In a graph-based synthesis using DD, the goal of optimization decreases representation space for boolean functions. This paper represents boolean functions using OPKFDD(Ordered Pseudo-Kronecker Functional Decision Diagrams) for a graph-based synthesis and is based on the number of nodes as the criterion of DD size. For a property of OPKFDD that is able to select one of different decomposition types for each node, OPKFDD is variable in its size by the decomposition types selection of each node and input variable order. This paper proposes a method for generating OPKFDD efficiently from the current BDD(Binary Decision Diagram) Data structure and an algorithm for minimizing one. In the multiple output functions, the relations of each function affect the number of nodes of OPKFDD. Therefore this paper proposes a method to decide the input variable order considering the above cases. Experimental results of comparing with the current representation methods and the reordering methods for deciding input variable order are shown.