The method of the First Derivative usually fails to detect overlapped peaks, especially when they appear as shoulders of the main one. Furthermore, the determination of the position of the maximum with this method is based on a single point, and it is highly dependent of the noise level of the experimental data. In this work, we propose an easy method to accurately estimate peak positions, based on a linearization of Gaussian curves. The method, which we called Natural Logarithm Derivative Method (NLDM), is also able to detect to a certain extent overlapping peaks, even when appearing as shoulders. Several factors such as the Lorentzian influence in the peak shape, the experimental error in the numerical calculations, or the minimum separation between peaks in order to be properly resolved are studied. The method is assayed with real samples, demonstrating the possibility of finding overlapping peaks in dyes, and in mixtures of dyes.