The main result obtained is the following: If a population has monotone decreasing correlogram, then centered systematic sampling is more efficient than random start systematic sampling. It is also shown that if a population is monotonic, then centered systematic sampling is more efficient than random start systematic sampling, but here it is easy to cite cases in which stratified random sampling is more efficient than either. Thus, centered systematic sampling is more efficient than random start systematic sampling, in the conditions (namely, concave upwards and decreasing correlogram) in which Cochran [1] proved that random start systematic sampling is more efficient than stratified random sampling.