||In this paper, we suggest a least squares procedure for the determination of the number of upper or lower outliers in normal sample by minimizing sample mean squares error. Moreover, the method free from the effects of masking and swamping, when testing upper or lower outliers in normal samples. In addition, we have also found that the least squares procedure is easy and simple to compute than test procedure Tk suggested by Zhang and Wang (1998) for determining the number of upper or lower outliers, since they need to use the complicated null distribution of Tk. Furthermore, we also correct of the upper bound of the significance probability of Tk suggested by them. Finally, we give two examples to study the practical performance of the procedures.