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⊆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)=V1∪V2　such　that　min{e(V1,V2),e(V2,V1)}≥(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).　©　2019　Elsevier　Ltd