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Current models of Titan's ionosphere have difficulties in explaining the observed electron density and/or temperature. In order to get new insights, we re-analyzed the data taken in the ionosphere of Titan by the Cassini Langmuir probe (LP), part of the Radio and Plasma Wave Science (RPWS) instrument. This is the first of two papers that present the new analysis method (current paper) and statistics on the whole data set. We suggest that between two and four electron populations are necessary to fit the data. Each population is defined by a potential, an electron density and an electron temperature and is easily visualized by a distinct peak in the second derivative of the electron current, which is physically related to the electron energy distribution function (Druyvesteyn method). The detected populations vary with solar illumination and altitude. We suggest that the four electron populations are due to photo-ionization, magnetospheric particles, dusty plasma and electron emission from the probe boom, respectively.