We introduce RedDebate, a novel multi-agent debate framework that provides the foundation for Large Language Models (LLMs) to identify and mitigate their unsafe behaviours. AI safety approaches often rely on costly human evaluation or isolated single-model assessment, both constrained by scalability and prone to oversight failures. RedDebate employs collaborative argumentation among multiple LLMs across diverse debate scenarios, enabling them to critically evaluate one another's reasoning and systematically uncover unsafe failure modes through fully automated red-teaming. To support this, we propose designing distinct long-term memory modules that preserve safety-relevant insights from debate interactions and leverage them during subsequent inference, facilitating continuous refinement of model behaviour. Empirical evaluation on safety benchmarks across a diverse set of models demonstrates that RedDebate substantially reduces unsafe outputs. While debate alone allows LLMs to refine their behaviour, the addition of memory yields further error reductions. To the best of our knowledge, RedDebate is the first fully automated framework to unify multi-agent debate and red-teaming to progressively enhance LLM safety without human intervention.