Context. The chemical tagging technique is a promising approach to reconstruct the history of the Galaxy by only using stellar chemical abundances. Different studies have undertaken this analysis and they raised several challenges. Aims. Using a sample of open clusters stars, we wish to address two issues: minimize chemical abundance differences which origin is linked to the evolutionary stage of the stars and not their original composition; evaluate a phylogenetic approach to group stars based

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... on their chemical composition. Methods. We derived differential chemical abundances for 207 stars (belonging to 34 open clusters) using the Sun as reference star (classical approach) and a dwarf plus a giant star from the open cluster M67 as reference (new approach). These abundances were then used to perform two phylogenetic analyses, cladistics (Maximum Parsimony) and Neighbour-Joining, together with a partitioning unsupervised classification analysis with k-means. The resulting groupings were finally confronted to the true open cluster memberships of the stars. Results. We successfully reconstruct most of the original open clusters when carefully selecting a subset of the abundances derived differentially with respect to M67. We find a set of eight chemical elements that yields the best result, and discuss the possible reasons for them to be good tracers of the history of the Galaxy. Conclusions. Our study shows that unraveling the history of the Galaxy by only using stellar chemical abundances is greatly improved provided that i) we perform a differential spectroscopic analysis with respect to an open cluster instead of the Sun, ii) select the chemical elements that are good tracers of the history of the Galaxy, and iii) use tools that are adapted to detect evolutionary tracks such as phylogenetic approaches.