Jackknifing is a nonparametric method of reducing bias in estimation procedures. The reduced-bias jackknife estimate is not, in general, a minimum variance (MV) estimate. The generalized jackknife is extended to allow the computation of jackknife estimates that are reduced in variance as compared with the usual jackknife estimate. The extended method is applicable in situations where there is information available on the covariance function of the given data set. This improved estimation procedure will then produce an approximately MV, reduced- bias estimate for any nonlinear function of the data. For linear combinations of the data, it is shown that the estimator reduces, as a special case, to an exactly MV, unbiased estimator.