The increasing number of transiting exoplanets sparked a significant interest in discovering their moons. Most of the methods in the literature utilize timing analysis of the raw light curves. Here we propose a new approach for the direct detection of a moon in the transit light curves via the so-called scatter peak. The essence of the method is the evaluation of the local scatter in the folded light curves of many transits. We test the ability of this method with different simulations: Kepler ‘short cadence’, Kepler ‘long cadence’, ground-based millimagnitude photometry with 3-min cadence and the expected data quality of the ESA planned planetary transits and oscillations of stars (PLATO) mission. The method requires ≈100 transit observations, therefore, applicable for moons of 10–20 d period planets, assuming 3–5 year long observing campaigns with space observatories. The success rate for finding a 1REarth moon around an 1RJupiter exoplanet turned out to be quite promising even for the simulated ground-based observations, while the detection limit of the expected PLATO data is around 0.4REarth. We give practical suggestions for observations and data reduction to improve the chance of such a detection: (i) transit observations must include out-of-transit phases before and after a transit, spanning at least the same duration as the transit itself, and (ii) any trend filtering must be done in such a way that the preceding and following out-of-transit phases remain unaffected.