In this paper, we develop a new ensemble construction algorithm (EUSBoost) based on RUSBoost, one of the simplest and most accurate ensemble, which combines random undersampling with Boosting algorithm. Our methodology aims to improve the existing proposals enhancing the performance of the base classifiers by the usage of the evolutionary undersampling approach. Besides, we promote diversity favoring the usage of different subsets of majority class instances to train each base classifier. Centered on two-class highly imbalanced problems, we will prove, supported by the proper statistical analysis, that EUSBoost is able to outperform the state-of-the-art methods based on ensembles. We will also analyze its advantages using kappa-error diagrams, which we adapt to the imbalanced scenario.