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Changes in extreme precipitation due to climate change often require the application of methods to bias correct simulated atmospheric fields, including extremes. Most existing bias correction techniques (i) only focus on the bias in the mean value or on the extreme values separately, and (ii) exclude zero values from analysis, even though their presence is significant in daily precipitation. We developed a copula-based bias correction scheme that is suitable for zero-inflated daily precipitation data to correct the bias in mean as well as in extreme precipitation at any specific statistical quantile. In considering the whole of Germany as a test bed, the proposed scheme is found to work well across the entire study area, including the German Alpine regions. The joint distribution between observed and regional climate model (RCM)-derived precipitation is developed through copulas. In particular, the joint distribution is modified to make it discrete at zero in order to account for zero values. The benefit of considering zero precipitation values is revealed through the improved performance of bias correction both in the mean and extreme values. Second, the quantile that best captures the bias (whether in the mean or any extreme value) is determined for a specific location and varies spatially and seasonally. This relaxation in selecting the location-specific optimal quantile renders the proposed methodology spatially transferable. By acknowledging possible changes in extreme precipitation due to climate change, the proposed scheme is expected to be suitable for climate change impact assessments for extreme events worldwide.