In this paper, we introduce a method of analysis of the dielectric relaxation data, which results to be very suitable for studying the coalescence of the alpha and beta processes in the time domain. We show that, at least in the case of the glass-forming liquid BCDE (bis-phenol-C-dimethylether), the coalescence process can be well described by assuming that both, the alpha and beta processes, behave as statistically independent processes. This simple assumption allows to describe the coalescence range of the two processes by extrapolating the low temperature behavior (where both processes are well separated), contrary to more classical approaches in which one needs to introduce a temperature at which the mechanism of the beta process changes.