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The mirror tree is a method to predict protein-protein interaction by evaluating the similarity between distance matrices of proteins. It is known, however, that predictions by the mirror tree method include many false positives. We suspected that the information about the evolutionary relationship of source organisms may be the cause of the false positives, because the information is shared by the distance matrices. Therefore, we excluded the information from the distance matrices and evaluated the similarity of the residuals as the intensity of co-evolution. We developed two different methods with a projection operation and partial correlation coefficient. The number of false positives were drastically reduced by our methods.