Degeneracy in transportation problems is a frequent phenomenon. In this paper, a method of obtaining optimal solutions to degenerate transportation problems has been suggested. The method is a modification of the already-known Modified Distribution (MODI) method and consists in proceeding with the non-zero cells of the basis and a dual solution corresponding to these cells—without attempting to complete the basis. It appears that the method proposed here would be more effective than the well-known perturbation method, especially when the problem is highly degenerate.