AbstractIn the use of systematic sampling in surveys it is known that the effect of negative correlations (=ϱwst) between deviations from stratum means of pairs of items in the same systematic sample is such that the resulting variance V(ȳst) can be zero for systematic sample means ȳst (e.g., Cochran, 1977, ch. 8). For such populations systematic sampling is then superior both to stratified sampling (one unit per stratum) and to simple random sampling.Cochran (loc. cit.) does not identify special types of finite populations for which ϱwst = −1/(n ‐1) and hence V(ȳst) =0. It is the purpose of this paper to present one type of population for which this condition is satisfied.