This study deals with the statistical properties of a randomization test applied to an ABAB design in cases where the desirable random assignment of the points of change in phase is not possible. In order to obtain information about each possible data division we carried out a conditional Monte Carlo simulation with 100,000 samples for each systematically chosen triplet. Robustness and power are studied under several experimental conditions: different autocorrelation levels and different effect sizes, as well as different phase lengths determined by the points of change. Type I error rates were distorted by the presence of autocorrelation for the majority of data divisions. Satisfactory Type II error rates were obtained only for large treatment effects. The relationship between the lengths of the four phases appeared to be an important factor for the robustness and the power of the randomization test.