Detecting self-contradictions within documents is a challenging task for ensuring textual coherence and reliability. While large language models (LLMs) have advanced in many natural language understanding tasks, document-level self-contradiction detection (DSCD) remains insufficiently studied. Recent approaches leveraging Chain-of-Thought (CoT) prompting aim to enhance reasoning and interpretability; however, they only gain marginal improvement and often introduce inconsistencies across repeated responses. We observe that such inconsistency arises from incomplete reasoning chains that fail to include all relevant contradictory sentences consistently. To address this, we propose a two-stage method that combines supervised fine-tuning (SFT) and reinforcement learning (RL) to enhance DSCD performance. In the SFT phase, a teacher model helps the model learn reasoning patterns, while RL further refines its reasoning ability. Our method incorporates a task-specific reward function to expand the model's reasoning scope, boosting both accuracy and consistency. On the ContraDoc benchmark, our approach significantly boosts Llama 3.1-8B-Instruct's accuracy from 38.5% to 51.1%, and consistency from 59.6% to76.2%.