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The application of deep neural network models in various security-critical applications has raised significant security concerns, particularly the risk of backdoor attacks. Neural backdoors pose a serious security threat as they allow attackers to maliciously alter model behavior. While many defenses have been explored, existing approaches are often bounded by model-specific constraints, or necessitate complex alterations to the training process, or fall short against diverse backdoor attacks. In this work, we introduce a novel method for comprehensive and effective elimination of backdoors, called ULRL (short for UnLearn and ReLearn for backdoor removal). ULRL requires only a small set of clean samples and works effectively against all kinds of backdoors. It first applies unlearning for identifying suspicious neurons and then targeted neural weight tuning for backdoor mitigation (i.e., by promoting significant weight deviation on the suspicious neurons). Evaluated against 12 different types of backdoors, ULRL is shown to significantly outperform state-of-the-art methods in eliminating backdoors whilst preserving the model utility.