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In the present paper efforts have been made to arrive at the three-level NAND network of any general Boolean function by utilizing its complementary function. It has been shown that the knowledge of the complementing gates of the three-level NAND circuit with minimum number of gates in the AND level can readily be obtained from the study of the prime implicants of the complementary function. A reduced form of the Cover and Closure (CC) table is suggested which is applicable in the above three-level NAND network synthesis. The paper also deals with the recognition of the class of functions for which the use of the CC table may be avoided to obtain the same network.