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 valuation 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 planned ESA mission of PLATO. The method requires ~100 transit observations, therefore applicable for moons of 10-20 day period planets, assuming 3-4-5 year long observing campaigns with space observatories. The success rate for finding a 1 R_Earth moon around a 1 R_Jupiter 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 0.4 R_Earth. 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; (ii) any trend filtering must be done in such a way that the preceding and following out-of-transit phases remain unaffected.
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