In　this　paper,　by　seeking　the　zero　and　the　positive　entry　positions　of　the　solution,　we　provide　a　direct　method,　called　the　reduced　order　method,　for　solving　the　linear　complementarity　problem　with　an　M-matrix.　By　this　method,　the　linear　complementarity　problem　is　transformed　into　a　low　order　linear　complementarity　problem　with　some　low　order　linear　equations　and　the　solution　is　constructed　by　the　solution　of　the　low　order　linear　complementarity　problem　and　the　solutions　of　these　low　order　linear　equations　in　the　transformations.　In　order　to　show　the　accuracy　and　the　effectiveness　of　the　method,　the　corresponding　numerical　experiments　are　performed.