The backdoor or Trojan attack is a severe threat to deep neural networks (DNNs). Researchers find that DNNs trained on benign data and settings can also learn backdoor behaviors, which is known as the natural backdoor. Existing works on anti-backdoor learning are based on weak observations that the backdoor and benign behaviors can differentiate during training. An adaptive attack with slow poisoning can bypass such defenses. Moreover, these methods cannot defend natural backdoors. We found the fundamental differences between backdoor-related neurons and benign neurons: backdoor-related neurons form a hyperplane as the classification surface across input domains of all affected labels. By further analyzing the training process and model architectures, we found that piece-wise linear functions cause this hyperplane surface. In this paper, we design a novel training method that forces the training to avoid generating such hyperplanes and thus remove the injected backdoors. Our extensive experiments on five datasets against five state-of-the-art attacks and also benign training show that our method can outperform existing state-of-the-art defenses. On average, the ASR (attack success rate) of the models trained with NONE is 54.83 times lower than undefended models under standard poisoning backdoor attack and 1.75 times lower under the natural backdoor attack. Our code is available at https://github.com/RU-System-Software-and-Security/NONE.