In common climate model bias-correction procedures, temperature and precipitation are corrected separately, thereby degrading the dynamical link represented within the model. We propose a methodology that advances the state-of-the-art by correcting not just the 1D intensity distributions separately but the full two-dimensional statistical distribution. To assess the effectiveness of the proposed method, it is applied to the REMO regional climate model output using point measurements of hourly temperature and precipitation from 6 weather stations over Germany as observations. A standard cross-validation is performed by dividing the data into two nonoverlapping 15 year periods. Results show that the methodology effectively improves the temperature-precipitation copula in the validation period, unlike separate 1D temperature and precipitation corrections which, by construction, leave the copula unchanged. An unexpected result is that a relatively small number (<5) of temperature bins are required to achieve significant improvements in the copula. Results are similar for all stations.