Multiconlitron　is　a　general　framework　for　designing　piecewise　linear　classifiers,　but　it　may　contain　a　relatively　large　number　of　conlitrons　and　linear　functions.　Based　on　the　concept　of　maximal　convexly　separable　subset　(MCSS),　we　propose　alternating　multiconlitron　as　a　novel　framework　for　piecewise　linear　classification.　Using　the　support　alternating　multiconlitron　algorithm,　an　alternating　multiconlitron　can　be　constructed　as　a　series　of　conlitrons　alternately　from　a　subset　of　one　class　to　the　MCSS　of　the　other　class.　Experimental　results　show　that　in　practice　an　alternating　multiconlitron　generally　has　a　much　simpler　structure　than　a　corresponding　multiconlitron,　performing　very　fast　in　testing　phase　with　similar　or　better　accuracies.　(C)　2014　Elsevier　Ltd.　All　rights　reserved.