Inthispaper,wegiveaconvergencetheoremanderrorestimatesforaniterationmethodundernewKantorovitch-Ostrowskitypeconditionusingtheinformationofhigherderivativesatinitialpoints.Comparedwiththecorrespondingstudyin[3],theconvergencedeterminationisestablishedunderoneglobalcondition,insteadoftwo,onthefunction.