Within the framework of the European project ENSEMBLES (ensembles-based predictions of climate changes and their impacts) we explore the systematic bias in simulated monthly mean temperature and precipitation for an ensemble of thirteen regional climate models (RCMs). The models have been forced with the European Centre for Medium Range Weather Forecasting Reanalysis (ERA40) and are compared to a new high resolution gridded observational data set. We find that each model has a distinct systematic bias relating both temperature and precipitation bias to the observed mean. By excluding the twenty-five percent warmest and wettest months, respectively, we find that a derived second-order fit from the remaining months can be used to estimate the values of the excluded months. We demonstrate that the common assumption of bias cancellation (invariance) in climate change projections can have significant limitations when temperatures in the warmest months exceed 4–6 °C above present day conditions.