of the most demanding requirements. Efficient testable logic synthesis is one way to tackle the problem. To this end, this paper introduces a new fast efficient graph-based decomposition technique for Boolean functions in finite fields, which utilizes the data structure of the Multiple-Output Decision Diagrams (MODD). In particular, the proposed technique is based on finite fields and can decompose any N valued arbitrary function F into N distinct sets conjunctively and N-1 distinct sets disjunctively. The proposed technique is capable of generating testable circuits. The experimental results show that the proposed method is more economical in terms of literal count compared to existing approaches. Furthermore, we have shown that the basic block can be tested with eight test vectors. Key terms: Multiple-Output Decision Diagrams, testable, Galois Field, OBDD, Multipliers.