WewillconsideranextensionofadirectmethodduetoGriewankandReddienforthecomputationofdoublesymmetry-breakingturningpointswhichariseinthetwo-parameterdependentnonlinearproblemoftheformf(x,λ,μ)=0.Themethodproposedcouldproduceanextendedsystemwhichdoesnotintroducethenullvectorsasvariables,andcouldthereforereducethecomputationaleffortandstorage.Onenumericalexampleispresentedtodemonstratethatthemethodisefficient.