A mathematical model is presented for a multicomponent, two-stream, countercurrent mass exchanger with a finite number of stages. The model relates the outlet compositions to the inlet compositions and the flow rate ratio of the two streams going through the exchanger, as well as the number of stages in the exchanger. An iterative solution procedure employing this model is proposed for the mass exchanger design problem. The model requires solution of a polynomial equation whose roots may be complex. Bounds to the real roots of the polynomial have also been established. Two examples illustrating how the method is employed are presented. The second example demonstrates that the iterative procedure converges even in the complex domain, and that complex roots exist for a real column.