Classification of noisy data has been a longstanding topic in data mining and machine learning. Many scientists have proposed effective methods to detect and eliminate such data in diverse real-world datasets. In this paper, we deal with mislabeled instances in supervised learning, including majority voting filtering and consensus voting filtering. The majority voting procedure usually incorrectly identifies many correct instances as noisy, whereas the consensus voting procedure is not able to detect at all many noisy instances. Our new method minimizes the majority and consensus filtering weaknesses by providing a novel class noise detection strategy, namely a high agreement voting filtering with mixed strategy, which proceeds by removing strong and semi-strong noisy records from the dataset as well as by relabeling weak noisy data. The proposed method, designed for binary classification problems, outperforms the high agreement voting filtering procedure. Extensive experiments conducted with 16 real datasets, using four noise filtering methods with two levels of class noise (10% and 15%), prove the superiority of the proposed methodology.