Spjotvoll [1967] has obtained a test associated with an unbalanced oneway layout for Model II ANOVA. Under the assumption of normality, his test possesses several optimum properties. Without the normality assumption, the significance level is (in general) highly nonrobust. An attempt to remedy this situation, using a test based on the jackknife technique, appears in Arvesen [1969]. The present paper proposes as an alternative a jackknifed version of Spjotvoll's test. The new test is not sensitive to departures from normality, and Monte Carlo sampling and asymptotic efficiency results suggest that it is more powerful than Arvesen's test. The paper also includes some general results for use of the jackknife technique with nonidentically distributed random variables.