Here we report on estimates of the changes in stratospheric water vapour (SWV) due to methane oxidation based on observational data. Above the tropopause oxidation of methane results in a decrease in its mixing ratio with altitude and this is a major source for SWV. The vertical profile of SWV changes from methane oxidation is presented here using satellite observations of the vertical profile of methane. Trends in the SWV are shown to be small in the lower stratosphere, but can reach 0.7 ppbv at 30 km at high latitudes over the period 1950--2000. The radiative forcing for this indirect effect of methane increase over the industrial era is estimated to be slightly weaker than 0.1 Wm-2 which implies a larger contribution of water vapour to the methane global warming potential than used in recent Intergovernmental Panel on Climate Change assessments. Our estimate considers only chemical changes and not SWV of dynamical causes. Importantly, we find substantial differences in the temperature change in the stratosphere for a homogeneous change in SWV and SWV change from methane oxidation. This has implications for trend analysis of SWV and understanding and attribution of the stratospheric temperature trend.