Transformer-based language models achieve state-of-the-art results on several natural language processing tasks. One of these is textual entailment, i.e., the task of determining whether a premise logically entails a hypothesis. However, the models perform poorly on this task when the examples contain negations. In this paper, we propose a new definition of textual entailment that captures also negation. This allows us to develop TINA (Textual Inference with Negation Augmentation), a principled technique for negated data augmentation that can be combined with the unlikelihood loss function. Our experiments with different transformer-based models show that our method can significantly improve the performance of the models on textual entailment datasets with negation-without sacrificing performance on datasets without negation.