Negation is a common linguistic feature that is crucial in many language understanding tasks, yet it remains a hard problem due to diversity in its expression in different types of text. Recent works show that state-of-the-art NLP models underperform on samples containing negation in various tasks, and that negation detection models do not transfer well across domains. We propose a new negation-focused pre-training strategy, involving targeted data augmentation and negation masking, to better incorporate negation information into language models. Extensive experiments on common benchmarks show that our proposed approach improves negation detection performance and generalizability over the strong baseline NegBERT (Khandelwal and Sawant, 2020).