Suppose　that　sigma　is　a　signed　graph　with　n　vertices　and　m　edges.　Let　lambda　1　＞　lambda　2　＞　.　.　.　＞　lambda　n　be　the　eigenvalues　of　sigma.　A　signed　graph　is　called　balanced　if　each　of　its　cycles　contains　an　even　number　of　negative　edges,　and　unbalanced　otherwise.　Let　wb　be　the　balanced　clique　number　of　sigma,　which　is　the　maximum　order　of　a　balanced　complete　subgraph　of　sigma.　In　this　paper,　we　prove　that　lambda　1　＜=　root　2　omega　b　-　1/omega　bm.　This　inequality　extends　a　conjecture　of　ordinary　graphs,　which　was　confirmed　by　Nikiforov　(2002)　[8],　to　the　signed　case.　In　addition,　we　completely　characterize　the　signed　graphs　with　-1　＜　lambda　2　＜　0.(c)　2022　Elsevier　Inc.　All　rights　reserved.