Unknown examples that are unseen during training often appear in real-world machine learning tasks, and an intelligent self-learning system should be able to distinguish between known and unknown examples. Accordingly, open set recognition (OSR), which addresses the problem of classifying knowns and identifying unknowns, has recently been highlighted. However, conventional deep neural networks using a softmax layer are vulnerable to overgeneralization, producing high confidence scores for unknowns. In this paper, we propose a simple OSR method based on the intuition that OSR performance can be maximized by setting strict and sophisticated decision boundaries that reject unknowns while maintaining satisfactory classification performance on knowns. For this purpose, a novel network structure is proposed, in which multiple one-vs-rest networks (OVRNs) follow a convolutional neural network feature extractor. Here, the OVRN is a simple feed-forward neural network that enhances the ability to reject nonmatches by learning class-specific discriminative features. Furthermore, the collective decision score is modeled by combining the multiple decisions reached by the OVRNs to alleviate overgeneralization. Extensive experiments were conducted on various datasets, and the experimental results showed that the proposed method performed significantly better than the state-of-the-art methods by effectively reducing overgeneralization.