For　structural　damage,　the　flexibility　is　more　sensitive　than　its　frequency　or　mode.　The　curvature　difference　matrix　in　flexibility　is　presented　as　a　new　index　of　nondestructive　damage　detection,　derived　from　the　change　in　structural　flexibilities　calculated　before　damaging　and　after　damaging　by　means　of　difference　calculation　twice,　firstly　to　columns,　and　then　to　rows.　Therefore　a　new　indicator　called　δ　Flexibility　Curvature　Matrix　Diagonal　(δ　FCMD)　is　constructed　through　principal　diagonal　elements　based　on　the　curvature　difference　matrix　in　flexibility.　Numerical　simulation　examples　indicate　that　the　damage　location　and　severity　in　structures,　with　single　damage,　multiple　ones,　lighter　ones　and　ones　at　the　supports,　can　be　detected　efficiently　for　cantilever　beams,　fixed　supported　beams,　simply　supported　beams,　continuous　beams　and　so　on　by　δ　FCMD　through　only　a　few　of　the　lower　order　modes.　Compared　to　the　aforementioned　flexibility　indicators　and　δ　FCMD,　such　as　the　change　in　flexibility,　the　rate　in　flexibility,　the　curvature　change　in　uniform　load　surface　(ULSC),　the　effectiveness　and　advantage　of　δ　FCMD,　etc　are　shown.