The　local　search　algorithm　for　the　capacitated　max-k-cut　problem　proposed　by　Gaur　et　al.　(2008)　is　not　guaranteed　to　terminate.　In　this　note,　we　modify　the　iterative　step　of　their　algorithm　to　make　it　terminate　in　a　finite　number　of　steps.　The　modified　algorithm　is　pseudo-polynomial,　and　in　a　special　case　it　is　strongly　polynomial.　Moreover,　we　analyze　the　worst　case　bound　of　the　modified　algorithm　and　give　some　extensions.