This paper proposes an algorithm that seeks the optimal solution for an assignment problem through a simplified process. Generally it is Hungarian algorithm that is prevalently used to solve a given assignment problem. The proposed algorithm reduces 4 steps Hungarian algorithm into 2 steps. Firstly, the algorithm selects the minimum cost from a matrix and deletes the rest of the rows and columns. Secondly, it improves on the solution through reassignment process. For 27 balanced assignment problems and 7 unbalanced problems, the proposed algorithm has successfully yielded the optimal solution, which Genetic algorithm has failed. This algorithm is thus found to be an appropriate replacement of Hungarian algorithm.