Chatterjee＇s　new　coefficient　proposed　by　Chatterjee　[2021,　＇A　New　Coefficient　of　Correlation＇,　Journal　of　the　American　Statistical　Association,　116(536),　2009-2022.]　is　used　to　measure　the　degree　of　dependence　between　two　scalars　by　rank　correlation.　However,　the　independence　test　based　on　Chatterjee＇s　rank　correlation　may　lose　power　since　it　only　considers　the　distance　between　the　nearest　neighbours　and　ignores　the　other　neighbours.　In　this　paper,　we　propose　an　improvement　to　Chatterjee＇s　new　coefficient　by　incorporating　the　inverse　distance-weighting,　and　further　obtain　the　asymptotic　normality　of　the　improved　coefficient　and　the　Berry-Esseen　bound　under　the　null　hypothesis.　The　proposed　method　is　evaluated　on　the　simulated　as　well　as　the　real　data　on　Yeast　Gene　Expression.　The　results　show　that　the　proposed　method　is　superior　to　Chatterjee＇s　new　coefficient　under　various　alternative　hypotheses.