Two graphic holistic metrics for assessing the greenness of synthesis, the "green star" and the "green circle", have been presented previously. These metrics assess the greenness by the degree of accomplishment of each of the 12 principles of green chemistry that apply to the case under evaluation. The criteria for assessment were based on the hazards symbols used in the system established by the European Union, directive 67/548/EEC, obtained from the safety data sheets of chemicals. Meanwhile, the Globally Harmonized System of Classification and Labeling of Chemicals (GHS) replaced that system and introduced a new classification of hazards and new symbols. The objective of this work is to present new criteria for the construction of the metrics based on the GHS system. A brief presentation of this system is included. The present upgrade also includes an improvement of the graphic presentation of the green star to facilitate the visual assessment of the degree of accomplishment of each green chemistry principle.