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The bias correction of the General Circulation Model (GCM) outputs has become a routine step that is taken in climate change impact assessments. To responsibly support the decision-making processes, the climate-modeling community has been debating about the conceptual requirements that bias-correction methods should fulfill. Bearing in mind these requirements, we propose to decompose atmospheric variables into three temporal elements that represent the climate mean state, the interannual variability, and the daily variability. This decomposition is aimed at correcting the biases at one time scale without affecting the simulated climate (mean state) trend or the distributional properties at other time scales. The novelty of the proposed approach is, nevertheless, marked by the adjustment of interannual and daily variability that is made by replacing the GCM-simulated data with synthetic samples drawn from Stable Distributions (SDs) that are fitted to the observed variability. The replacement prevents the transfer of the sampling variability of the calibration period and gives the corrected data the distributional properties of the observed climate. The employment of SDs was motivated by the fact that the climate-change-induced changes in the scale, the symmetry, and the frequency of extremes can be measured and applied to the SDs of the observed data. We correct the biases in the GCM-simulated temperature and precipitation over northern South America using our proposed approach and two other existing ones. Our proposed method is capable of not only preserving the simulated climate trends but also reproducing the observed extremes as well as a more flexible method based on nonparametric distributions.