Cross　distance　minimization　algorithm　(CDMA)　is　an　iterative　method　for　designing　a　hard　margin　linear　SVM　based　on　the　nearest　point　pair　between　the　convex　hulls　of　two　linearly　separable　data　sets.　In　this　paper,　we　propose　a　new　version　of　CDMA　with　clear　explanation　of　its　linear　time　complexity.　Using　kernel　function　and　quadratic　cost,　we　extend　the　new　CDMA　to　its　kernel　version,　namely,　the　cross　kernel　distance　minimization　algorithm　(CKDMA),　which　has　the　requirement　of　linear　memory　storage　and　the　advantages　over　the　CDMA　including:　(1)　it　is　applicable　in　the　non-linear　case;　(2)　it　allows　violations　to　classify　non-separable　data　sets.　In　terms　of　testing　accuracy,　training　time,　and　number　of　support　vectors,　experimental　results　show　that　the　CKDMA　is　very　competitive　with　some　well-known　and　powerful　SVM　methods　such　as　nearest　point　algorithm　(NPA),　kernel　Schlesinger-Kozinec　(KSK)　algorithm　and　sequential　minimal　optimization　(SMO)　algorithm　implemented　in　LIBSVM2.9.