Abstract: Consistenoy of a slightly modified jackknife estimator of the asymptotio variance of a differentiable statistical functional is established. This modified jackknife estimator is shown to require less stringent eonditions for its consistency than the original jaokknife estimator in very general situations. The computation aspeot of the modified jackknife estimator is also eonsidered. An exampleis given to illustrate the application of the theory.