<p>An unbiased estimation of the variance of the sample mean or the population total is achievable only when the second-order inclusion probabilities are positive for all possible pairs of sampled units. In the conventional systematic sampling scheme, this condition is generally not satisfied, since some of the second-order inclusion probabilities turn out to be zero. In this study, a modified sampling strategy is proposed to overcome this limitation. Under the proposed approach, the population units are first arranged systematically into several groups. A systematic procedure is then applied again to select a subset of these groups. From the remaining groups, one group is chosen at random, and all the selected groups are finally combined to form the sample. This selection mechanism guarantees that the second–order inclusion probabilities remain positive for all pairs of units, which in turn allows an unbiased estimation of the variance of the sample mean or the total. The paper also presents a detailed comparison of the efficiency of the proposed method with existing systematic sampling schemes.</p>