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Deep Neural Networks (DNNs) have improved the accuracy of classification problems in lots of applications. One of the challenges in training a DNN is its need to be fed by an enriched dataset to increase its accuracy and avoid it suffering from overfitting. One way to improve the generalization of DNNs is to augment the training data with new synthesized adversarial samples. Recently, researchers have worked extensively to propose methods for data augmentation. In this paper, we generate adversarial samples to refine the Domains of Attraction (DoAs) of each class. In this approach, at each stage, we use the model learned by the primary and generated adversarial data (up to that stage) to manipulate the primary data in a way that look complicated to the DNN. The DNN is then retrained using the augmented data and then it again generates adversarial data that are hard to predict for itself. As the DNN tries to improve its accuracy by competing with itself (generating hard samples and then learning them), the technique is called Self-Competitive Neural Network (SCNN). To generate such samples, we pose the problem as an optimization task, where the network weights are fixed and use a gradient descent based method to synthesize adversarial samples that are on the boundary of their true labels and the nearest wrong labels. Our experimental results show that data augmentation using SCNNs can significantly increase the accuracy of the original network. As an example, we can mention improving the accuracy of a CNN trained with 1000 limited training data of MNIST dataset from 94.26% to 98.25%.