AbstractSrivastava (1980) has shown that Grubbs's (1950) test for a univariate outlier is robust against the effect of equicorrelation. In this note we extend Srivastava's result by giving a more general covariance structure, which relaxes both the covariance structure and the assumption of equal variances. We also show that under the more general covariance structure, the power of Grubbs's test, as well as the significance level, is identical to the independently and identically distributed case.