To　be　suitable　for　the　security　evaluation　of　non-interactive　deniable　authentication　protocol,　this　paper　re-defines　the　attribute　of　key-compromise　impersonation　(KCI)　as　the　attribute　of　sender　key-compromise　impersonation　(SKCI).　A　new　improved　scheme　is　then　proposed　for　solving　the　receiver　KCI　problem　of　Cao＇s　scheme.　Compared　with　the　old　scheme,　the　improved　scheme　saves　six　times　pairing　operations　and　its　both　sides　interactive　number　of　times　decreases　two　times.　In　addition,　the　proposed　scheme　does　not　need　an　addition　signature,　which　is　necessary　in　Liao＇s　improved　scheme,　to　provide　extra　authentication　and　simultaneously　satisfies　authenticity,　deniability　and　sender　key-compromise　impersonation　security　attributes.