A　signed　graph　G　is　a　graph　associated　with　a　mapping　σ:　E(G)→{+1,−1}.　An　edge　e∈E(G)　is　positive　if　σ(e)=1　and　negative　if　σ(e)=−1.　A　circuit　in　G　is　balanced　if　it　contains　an　even　number　of　negative　edges,　and　unbalanced　otherwise.　A　barbell　consists　of　two　unbalanced　circuits　joined　by　a　path.　A　signed　circuit　of　G　is　either　a　balanced　circuit　or　a　barbell.　A　signed　graph　is　coverable　if　each　edge　is　contained　in　some　signed　circuit.　An　oriented　signed　graph　(bidirected　graph)　has　a　nowhere-zero　integer　flow　if　and　only　if　it　is　coverable.　A　signed　circuit　cover　of　G　is　a　collection　F　of　signed　circuits　in　G　such　that　each　edge　e∈E(G)　is　contained　in　at　least　one　signed　circuit　of　F;　The　length　of　F　is　the　sum　of　the　lengths　of　the　signed　circuits　in　it.　The　minimum　length　of　a　signed　circuit　cover　of　G　is　denoted　by　scc(G).　The　first　nontrivial　bound　on　scc(G)　was　established　by　Máajová　et　al.,　who　proved　that　scc(G)≤11|E(G)|　for　every　coverable　signed　graph　G,　which　was　recently　improved　by　Cheng　et　al.　to　scc(G)≤[Formula　presented]|E(G)|.　In　this　paper,　we　prove　that　scc(G)≤[Formula　presented]|E(G)|　for　every　coverable　signed　graph　G.　©　2017　Elsevier　B.V.