Context. The analysis of non-variable stars is generally neglected in the literature. However, such objects are needed for many calibration processes and for testing pulsational models. The photometric time series of the Kepler satellite mission still stand as the most accurate data available today and are excellently suited to the search for non-variable stars. Aims. We analysed all long-cadence light curves for stars not reported as a variable so far from the Kepler satellite mission. Using the known characteristics and flaws of these data sets, we defined three different frequency ranges where we searched for non-variability. Methods. We used the Lomb–Scargle periodogram and the false-alarm probability (FAP) to analyse the cleaned data sets of 138 451 light curves. We then used log FAP ≥ −2 to define a star as ‘non-variable’ in the ranges below 0.1 c/d, 0.1 to 2.0 c/d, and 2.0 to 25.0 c/d, respectively. Furthermore, we also calculated the standard deviation of the mean light curve to obtain another parameter. Results. In total, we found 14 154 stars that fulfil the set criteria. These objects are mostly cooler than the 7000 K populating the whole main sequence (MS) to the red giant branch (RGB).