Abstract: A new method concerning how to eliminate leverage points with outliers from the conditional subset is considered.Firstly,several subsets of observations are selected randomly from all observations in accordance with the percentage of leverage points with outliers in order to obtain one subset containing no leverage points with outliers.Secondly,the conditional subset is selected from the subsets that are selected above according to the sum of squares of the residuals.Lastly,a new algorithm is given by connecting our procedure with the Gibbs sampling.