Global climate model (GCM) output typically needs to be bias corrected before it can be used for climate change impact studies. Three existing bias correction methods, and a new one developed here, are applied to daily maximum temperature and precipitation from 21 GCMs to investigate how different methods alter the climate change signal of the GCM. The quantile mapping (QM) and cumulative distribution function transform (CDF-t) bias correction methods can significantly alter the GCM’s mean climate change signal, with differences of up to 2°C and 30% points for monthly mean temperature and precipitation, respectively. Equidistant quantile matching (EDCDFm) bias correction preserves GCM changes in mean daily maximum temperature but not precipitation. An extension to EDCDFm termed PresRat is introduced, which generally preserves the GCM changes in mean precipitation. Another problem is that GCMs can have difficulty simulating variance as a function of frequency. To address this, a frequency-dependent bias correction method is introduced that is twice as effective as standard bias correction in reducing errors in the models’ simulation of variance as a function of frequency, and it does so without making any locations worse, unlike standard bias correction. Last, a preconditioning technique is introduced that improves the simulation of the annual cycle while still allowing the bias correction to take account of an entire season’s values at once.