We present five new discriminant function diagrams based on an extensive database representative of basic and ultrabasic rocks from four tectonic settings of island arc, continental rift, ocean-island, and mid-ocean ridge. These diagrams were obtained after loge-transformation of concentration ratios of major-elements — a technique recommended for a correct statistical treatment of compositional data. Higher % success rates (overall values from ∼ 83 to 97%) were obtained for proposing these new diagrams as compared to those (∼82 to 94%) obtained from the discriminant analysis of the raw major-element concentration data (i.e., without the loge-transformation and without taking ratios of the compositional data, but using exactly the same database to provide an unbiased comparison), suggesting that such a data transformation constitutes a statistically correct and recommended technique. The new diagrams also resulted in less mis-classification of basic and ultrabasic rocks from known tectonic settings than the diagrams obtained from the raw data. The use of these highly successful new discriminant function diagrams is illustrated using Miocene to Recent basic and ultrabasic rocks from three areas of Mexico with complex or controversial tectonic settings (Mexican Volcanic Belt, Los Tuxtlas volcanic field, and Eastern Alkaline Province), as well as older rocks from three areas (Deccan, Malani, and Bastar) of India. Additionally, the major-element data from two ‘known’ continental arc settings are used to show that they are similar to those from the island arc setting. Continental rift setting is inferred for all Mexican cases and for one cratonic area of India (Malani) and an IAB setting for the Bastar craton. The Deccan flood basalt province of India is used to warn against an indiscriminate use of those discrimination diagrams that do not explicitly include the likely setting of the area under evaluation. An Excel template is also provided for an easy application of these new diagrams for discriminating the four settings considered in this work.