Inthispaper,wesuggestasixthorderconvergencethree-stepmethodtosolvesystemofnonlinearequations.Everyiterationofthemethodrequirestwofunctionevaluations,twofirstFréchetderivativeevaluationsandtwomatrixinversions.Hence,theefficiencyindexis61/(2n+6n2+43n3),whichisbetterthanthatofothersixthordermethods.Theadvantagesofthemethodlieinthefeaturethatthistechniquenotonlyachievesanapproximatesolutionwithhighaccuracy,butalsoimprovesthecalculationspeed.Also,underseveralmildconditionstheconvergenceanalysisoftheproposedmethodisprovided.Anefficienterrorestimationispresentedfortheapproximatesolution.Numericalexamplesareincludedtodemonstratethevalidityandapplicabilityofthemethodandthecomparisonsaremadewiththeexistingresults.
