In a paper in this Journal, McMillan (1971) compared three procedures for the detection of outliers in samples from a Normal population. One of these was a sequential application of a maximum residual test. One step in McMillan's derivation of the probability of detecting two outliers using this test is incorrect. A correct derivation is presented in this note and some numerical results in McMillan's paper are appropriately amended. McMillan's qualitative statements on the performance of the test are essentially unaffected.