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The success of the local covering approach to multiple-valued input two-valued output (MVITVO) functions minimization depends greatly on the proper choice of the base minterms from the ON set of the new techniques developed to improve the performance of this approach. We have introduced a graph called an enhanced assignment graph (EAG) for the efficient grouping of the Boolean variables. In order to make the best choice of the proper base minterm we have defined a new technique to find the potential canonical cube (PCC) covering it. In this process, we have succeeded in finding out the essential primes efficiently which enhances the total computation time and produces better sum of products (SOP).