Summary: An outlier problem given by B. R. Clarke and T. Lewis [J. Appl. Stat. 25, 751-762 (1998; Zbl 0956.62018)] provides the motivation to develop a least squares procedure for outliers when observations are distributed with the same mean but different variances. The criterion of the proposed procedure is to minimize the error sum of squares. One advantage of the procedure is that it is more easy and more simple to compute than the test procedure R suggested by Clarke and Lewis, since they need to use the complicated null distribution of R. Furthermore, the method is free from the effects of masking and swamping, when testing upper or lower outliers in normal samples. Results from simulation studies assess that the performance of our proposed method is better than that of Clarke and Lewis’ procedure. Finally, we also use the proposed procedure to analyse ore grade data (see Table 1 of Clarke and Lewis’ paper).