In the current study, a new method by the weighting absolute centered external variable (WCEV) was proposed to stabilize heteroscedasticity for butterfly-distributed residuals (BDRs). After giving brief information about heteroscedasticity and BDRs, WCEV was introduced. The WCEV and commonly used variance stabilizing methods are compared on a simple and a multiple regression model. The WCEV was also tested for other type of heteroscedasticity patterns. In addition to heteroscedasticity, other regression assumptions were checked for the WCEV.