Phylogenetics is the study of the evolutionary relationships among different species through the analysis of sequences of biological data such as DNA. These relationships are usually represented using phylogenetic trees, which are tree diagrams that relate every species with its ancestor. Phylogenetic methods try to determine which tree best fits a given set of DNA sequences by using either distances among species or evolutionary models. In this line, the main goal of this project is to propose a new method for phylogenetic reconstruction, using a new coordinate system (Fourier coordinates), focused on 4-leaved trees under a certain evolutionary Markov model.