Projected changes in near-surface relative humidity (RH) remain highly model-dependent over land and may have been underestimated by the former generation global climate models. Here the focus in on the recent CNRM-CM6-1 model, which shows an enhanced land surface drying in response to quadrupled atmospheric CO2 compared to its CNRM-CM5 predecessor. Atmosphere-only experiments with prescribed sea surface temperature (SST) are used to decompose the simulated RH changes into separate responses to uniform SST warming, pattern of SST anomalies, changes in sea-ice concentration, as well as direct radiative and physiological CO2 effects. Results show that the strong drying simulated by CNRM-CM6-1 is due to both fast CO2 effects and a SST-mediated response. The enhanced drying compared to CNRM-CM5 is partly due to the introduction of the physiological CO2 effect that was not accounted for in CNRM-CM5. The global ocean warming also contributes to the RH decline over land, in reasonable agreement with the moisture advection mechanism proposed by earlier studies which however does not fully capture the contrasted RH response between the two CNRM models. The SST anomaly pattern is a significant driver of changes in RH humidity at the regional scale, which are partly explained by changes in atmospheric circulation. The improved land surface model may also contribute to a stronger soil moisture feedback in CNRM-CM6-1, which can amplify the surface aridity induced by global warming and, thereby, lead to a non-linear response of RH.