Structural　damage　detection　is　a　key　part　of　structural　health　monitoring.　The　generalized　flexibility　matrix　approach　is　an　effective　method　for　damage　detection.　Compared　with　the　flexibility　matrix　approach,　it　requires　less　number　of　natural　frequencies　and　corresponding　mode　shapes.　In　this　paper,　the　approach　is　improved　by　considering　the　nonnegativity　of　the　damage　extent.　The　error　bound　of　two　solutions　calculated　by　the　improved　approach　using　natural　frequencies　and　corresponding　mode　shapes　without　and　with　noises　is　derived.　Numerical　examples　with　different　damage　scenarios　show　that　compared　with　the　original　generalized　flexibility　matrix　approach,　our　proposed　method　works　better.