We would like first to stress that we have not "claimed" wide applicability for this method except for the results that we have given. Our motivation for carrying out this work was to find a method of locating and tracing negative cycles to use as a subroutine in Klein's [Klein, M. 1967. A primal method for minimal cost flows with applications to the assignment and transportation problems. Management Sci. 4 (3) 205-220.] algorithm.