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Variance estimation is an important aspect in statistical inference, especially in the dependent data situations. Resamplingmethods are ideal for solving this problem since these do not require restrictive distributional assumptions. In this paper, wedevelop a novel resampling method in the Jackknife family called the stationary jackknife. It can be used to estimatethe variance of a statistic in the cases where observations are from a general stationary sequence. Unlike the moving blockjackknife, the stationary jackknife computes the jackknife replication by deleting a variable length block and thelength has a truncated geometric distribution. Under appropriate assumptions, we can show the stationary jackknifevariance estimator is a consistent estimator for the case of the sample mean and, more generally, for a class of nonlinearstatistics. Further, the stationary jackknife is shown to provide reasonable variance estimation for a wider range ofexpected block lengths when compared with the moving block jackknife by simulation.