The　＂relative　entropy＂　has　been　used　as　a　minimization　function　to　predict　the　tertiary　structure　of　a　protein　backbone,　and　good　results　have　been　obtained.　However,　in　our　previous　work,　the　ensemble　average　of　the　contact　potential　was　estimated　by　an　approximate　calculation.　In　order　to　improve　the　theoretical　integrity　of　the　relative-entropy-based　method,　a　new　theoretical　calculation　method　of　the　ensemble　average　of　the　contact　potential　was　presented　in　this　work,　which　is　based　on　the　thermodynamic　perturbation　theory.　Tests　of　the　improved　algorithm　were　performed　on　twelve　small　proteins.　The　root　mean　square　deviations　of　the　predicted　versus　the　native　structures　from　Protein　Data　Bank　range　from　0.40　to　0.60　nm.　Compared　with　the　previous　approximate　values,　the　average　prediction　accuracy　is　improved　by　0.04　nm.