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A new method for solving the assignment problem based on the decomposition of the orig inal problem into a number of two dimensional optimization problems is proposed. The integer val uedness and monotonicity of the iterative procedure with respect to the objective function ensures that the algorithm is finite. As a result, either a unique optimal solution of the original assignment problem or a system of constraints is obtained. In the latter case, the system of constraints can be used to obtain all optimal solutions. Examples illustrating the algorithm are discussed.