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Non-stationarity is a major concern for statistically downscaling climate change scenarios for impact assessment. This study evaluates whether a statistical downscaling method is fully applicable to generate daily precipitation under non-stationary conditions in a wide range of climatic zones. Ten stations were selected from polar to tropical climates around the world. The measured data were split into calibration and validation periods in such a way that the difference of the mean annual precipitation between the two periods was maximized. Transition probabilities of wet-following-wet (Pw/w) and wet-following-dry (Pw/d) days generally increased linearly with an increase in mean monthly precipitation for all calendar months and locations in all climatic zones. The transition probabilities of the validation periods, interpolated with linear regressions, agreed well with those directly calculated from the observed data of the periods, with model efficiency ranging from 0.786 to 0.966. Due to good estimation of Pw/w and Pw/d, generated frequency distributions of dry and wet spell lengths agreed reasonably well with the measured distributions for the validation period. Overall, statistics of the downscaled daily and monthly precipitation amounts, annual maximum daily amounts, and dry and wet spells were similar to those of the measured data for stations whose skewness coefficients were not greater than 3.5, suggesting that caution be exercised when generating daily precipitation with the Pearson type III distribution if the skewness coefficient is greater than 3.5. This downscaling method can be easily used with the two-parameter gamma distribution for daily precipitation to circumvent the skewness issue, if necessary. This study has demonstrated that the downscaling method can generate proper daily precipitation series for climates having non-stationary changes.