The end portion of a wire wound noise preventing resistance cable in which a resistance wire is transversely wound around a core formed from an elastomeric compound is terminated such that the resistance wire is fully embedded in the core by applying heat and high pressure to the leading end that remains exposed after the cable is cut and the end portion thereof is stripped of a covering layer. This construction of the end portion of the core prevents unraveling of the resistance wire and maintains a good electrical connection between the resistance wire and a metal terminal.