AdaBoost is a highly popular ensemble classification method for which many variants have been published. This paper proposes a generic refinement of all of these AdaBoost variants. Instead of assigning weights based on the total error of the base classifiers (as in AdaBoost), our method uses class-specific error rates. On instance x it assigns a higher weight to a classifier predicting label y on x, if that classifier is less likely to make a mistake when it predicts class y. Like AdaBoost, our method is guaranteed to boost weak learners into strong learners. An empirical study on AdaBoost and one of its multi-class versions, SAMME, demonstrates the superiority of our method on datasets with more than 1,000 instances as well as on datasets with more than three classes.