Deep learning has outperformed other machine learning algorithms in a variety of tasks, and as a result, it is widely used. However, like other machine learning algorithms, deep learning, and convolutional neural networks (CNNs) in particular, perform worse when the data sets present label noise. Therefore, it is important to develop algorithms that help the training of deep networks and their generalization to noise-free test sets. In this paper, we propose a robust training strategy against label noise, called RAFNI, that can be used with any CNN. This algorithm filters and relabels instances of the training set based on the predictions and their probabilities made by the backbone neural network during the training process. That way, this algorithm improves the generalization ability of the CNN on its own. RAFNI consists of three mechanisms: two mechanisms that filter instances and one mechanism that relabels instances. In addition, it does not suppose that the noise rate is known nor does it need to be estimated. We evaluated our algorithm using different data sets of several sizes and characteristics. We also compared it with state-of-the-art models using the CIFAR10 and CIFAR100 benchmarks under different types and rates of label noise and found that RAFNI achieves better results in most cases.