Multi-agent debate systems are designed to derive accurate and consistent conclusions through adversarial interactions among agents. However, these systems often encounter challenges due to cognitive constraints, manifesting as (1) agents' obstinate adherence to incorrect viewpoints and (2) their propensity to abandon correct viewpoints. These issues are primarily responsible for the ineffectiveness of such debates. Addressing the challenge of cognitive constraints, we introduce a novel framework, the Multi-Agent Debate with Retrieval Augmented (MADRA). MADRA incorporates retrieval of prior knowledge into the debate process, effectively breaking cognitive constraints and enhancing the agents' reasoning capabilities. Furthermore, we have developed a self-selection module within this framework, enabling agents to autonomously select pertinent evidence, thereby minimizing the impact of irrelevant or noisy data. We have comprehensively tested and analyzed MADRA across six diverse datasets. The experimental results demonstrate that our approach significantly enhances performance across various tasks, proving the effectiveness of our proposed method.