Let　D　be　a　directed　graph.　The　minimum　semidegree　of　D　is　defined　to　be　the　minimum　value　of　the　minimum　outdegree　and　the　minimum　indegree　of　D.　For　nonempty　sets　S,　T　subset　of　V(D),　we　use　e(S,　T)　to　denote　the　number　of　arcs　in　D　from　S　to　T.　If　D　has　m　arcs　and　positive　minimum　semidegree,　then　we　show　that　D　admits　a　bipartition　V(D)　=　V-1　U　V-2　such　that　min{e(V-1,　V-2),　e(V-2,　V-1)}　＞=　(1/6　o(1))m.　We　also　prove　that　if　the　minimum　semidegree　is　at　least　two　(or　three,　respectively),　then　the　constant　can　be　increased　to　1/5　(or　3/14,　respectively).　These　partly　answer　a　question　of　Hou　and　Wu　(2018).　(C)　2019　Elsevier　Ltd.　All　rights　reserved.