A　digraph　D　is　supereulerian　if　D　has　a　spanning　directed　eulerian　subdigraph.　Hong　et　al.　proved　that　δ+(D)+δ-(D)≥|V(D)|-4　implies　D　is　supereulerian　except　some　well-characterized　digraph　classes　if　the　minimum　degree　is　large　enough.　In　this　paper,　we　characterize　the　digraphs　D　which　are　not　supereulerian　under　the　condition　dD+(u)+dD-(v)≥|V(D)|-4　for　any　pair　of　vertices　u　and　v　with　uv　∉A(D)　without　the　minimum　degree　constraint.　©　2016　Elsevier　B.V.　All　rights　reserved.