In the study of outlier identification in linear-circular regression, a new method, called the CDBER method, is introduced to enhance the accuracy and reliability of detecting outliers. This method measures the circular distance of each error value. The CDBER method is compared to the approach proposed by Sert & Kardiyen (2023) through extensive simulations on datasets both with and without outlier contamination. The evaluation is based on three metrics: probability of successfully detecting all outliers, masking effect, and swamping effect, to assess effectiveness under various conditions. The results indicate that the CDBER method generally performs well, though it may occasionally misclassify some inliers as outliers.