The　strength　reduction　method　(SRM)　is　becoming　more　and　more　popular　in　the　stability　analysis　of　slopes.　Nevertheless,　the　criterion　for　slope　failure　associated　with　SRM　is　controversial,　and　divergence　exists　while　approaching　to　the　limit　equilibrium　state　of　slopes.　In　this　study,　the　slip　body　is　discretized　with　constant　boundary　elements.　Since　at　least　one　element　on　the　slip　surface,　referred　to　as　the　critical　element,　should　keep　still　till　the　slope　reaches　the　limit　equilibrium　state,　the　critical　element　is　forced　to　be　fixed　throughout　while　other　elements　on　the　slip　surface　are　specified　to　be　contact　elements　during　the　strength　reduction.　In　this　way,　convergence　is　always　assured　in　the　open-close　iteration　of　contact　between　the　slip　body　and　the　slip　bed,　no　matter　how　much　the　strength　of　the　slip　surface　is　reduced.　The　limit　equilibrium　state　is　defined　to　be　the　moment　at　which　the　strength　redundancy　of　the　critical　element　vanishes.　The　method　of　bisection　is　applied　to　find　out　the　factor　of　safety　(FOS).　The　proposed　method　is　applied　to　those　benchmark　examples　and　the　comparison　is　made　with　the　limit　equilibrium　methods　(LEM).