Multiconlitron　is　a　general　framework　for　constructing　piecewise　linear　classifiers.　For　convexly　separable　and　commonly　separable　data　sets,　it　can　separate　them　correctly　by　using　support　conlitron　algorithm　(SCA)　and　support　multiconlitron　algorithm　(SMA),　respectively.　On　this　basis,　the　paper　proposes　a　maximal　cutting　construction　method　for　multiconlitron　design.　The　method　consists　of　two　training　processes.　In　the　first　step,　the　maximal　cutting　process　(MCP)　is　utilized　iteratively　to　find　a　linear　boundary　such　that　it　can　obtain　the　maximum　number　of　samples.　Thus,　the　MCP　can　reduce　the　number　of　linear　boundaries　and　construct　a　minimal　set　of　decision　functions,　and　ultimately　simplify　the　classifiation　model.　To　improve　the　generalization　ability　further,　in　the　second　step　we　employ　a　boundary　adjusting　process　(BAP)　to　make　the　classifiation　boundaries　more　fittable.　Experiments　on　both　synthetic　and　real　data　sets　show　that　the　presented　method　can　produce　more　reasonable　multiconlitron　with　better　performance.　Comparison　with　some　other　piecewise　linear　classifiers　verifies　its　effctiveness　and　competitiveness.　©　2014　Acta　Automatica　Sinica.　All　rights　reserved.