A statistical bias correction technique is applied to twelve high-resolution climate change simulations of temperature and precipitation over Europe, under the SRES A1B scenario, produced for the EU project ENSEMBLES. The bias correction technique is based on a transfer function, estimated on current climate, which affects the whole Probability Distribution Function (PDF) of variables, and which is assumed constant between the current and future climate. The impact of bias correction on 21st Century projections, their inter-model variability, and the climate change signal is investigated, with focus being on discrepancies between the original and the bias-corrected results. As assessing the impact of climate change is significantly dependent on the frequency of extreme events, we also analyze the evolution of the shape of the PDFs, and extreme events indices. Results show that the ensemble mean climate change signal and its inter-model variability are generally conserved. However, the impact of the bias correction varies amongst regions, seasons and models, and differences up to 0.5 C for the summer temperature climate change signal are found in Southern Europe. Finally the bias correction is found to influence the probability of extreme events like extremely hot or frost days, which also impacts the climate change signal.