Motivation Monotonic bivariate classifiers can describe simple patterns in high-dimensional data that may not be discernible using only elementary linear decision boundaries. Such classifiers are relatively simple, easy to interpret, and do not require large amounts of data to be effective. A challenge is that finding optimal pairs of features from a vast number of possible pairs tends to be computationally intensive, limiting the applicability of these classifiers. Results We prove a simple mathematical inequality and show how it can be exploited for the faster identification of optimal feature combinations. Our empirical results suggest speedups of 10x--20x, relative to the previous, naive, approach in applications. This result thus greatly extends the range of possible applications for bivariate monotonic classifiers. In addition, we provide the first open-source code to identify optimal monotonic bivariate classifiers. Availability: https://gitlab.pasteur.fr/ofourque/mem_python