We design, apply, and validate a methodology for correcting climate model output to produce internally consistent fields that have the same statistical intensity distribution as the observations. We refer to this as a statistical bias correction. Validation of the methodology is carried out using daily precipitation fields, defined over Europe, from the ENSEMBLES climate model dataset. The bias correction is calculated using data from 1961 to 1970, without distinguishing between seasons, and applied to seasonal data from 1991 to 2000. This choice of time periods is made to maximize the lag between calibration and validation within the ERA40 reanalysis period. Results show that the method performs unexpectedly well. Not only are the mean and other moments of the intensity distribution improved, as expected, but so are a drought and a heavy precipitation index, which depend on the autocorrelation spectra. Given that the corrections were derived without seasonal distinction and are based solely on intensity distributions, a statistical quantity oblivious of temporal correlations, it is encouraging to find that the improvements are present even when seasons and temporal statistics are considered. This encourages the application of this method to multi-decadal climate projections.