This article presents the first and second moments of an estimator which might be used when two subsamples are characterized by the same regression coefficients, but possibly different error variances. The estimator is the OLS estimator if the hypothesis of equal variances is accepted and the two-step Aitken estimator otherwise. The estimator is similar to one suggested by Goldfeld and Quandt and is applicable to a reparameterized version of the error components model.