Context. The detection of planets around other stars by the measurement of the stellar Radial Velocity (RV) variations benefits from improvements of dedicated spectrographs, allowing to achieve a precision of 1 ms −1 or better. Spectral intervals within which stellar lines are contaminated by telluric lines are classically excluded from the RV processing. Aims. We aim at estimating the potential improvement of telluric absorption removal and subsequent extension of the useful spectral domain on the precision of radial velocity measurements. Methods. We developed a correction method based on the on-line web service TAPAS, allowing to determine a synthetic atmospheric transmission spectrum for the time and location of observations. This method was applied to the telluric H 2 O and O 2 absorption removal from a series of 200 ESPRESSO consecutive exposures of the K2.5V star HD40307, available in ESO archives. We calculated the radial velocity using the standard Cross-Correlation Function (CCF) method and Gaussian fit of the CCF, with uncorrected spectra and the ESPRESSO standard stellar binary mask on one hand, and telluric-corrected spectra and an augmented binary mask with 696 additional lines on the other hand. Results. We find that the precision of radial velocity measurements is improved in the second case, with a reduction of the average formal error from 1.04 ms −1 down to 0.78 ms −1 in the case of these ESPRESSO data and this stellar type for the red arm. Using an estimator of the minimal error based on photon noise limit applied to the full CCF, the error is reduced from 0.89 ms −1 down to 0.78 ms −1 . This corresponds to a significant decrease of about 35% of observing time to reach the same precision in the red part.