Federated Unlearning (FU) enables clients to selectively remove the influence of specific data from a trained federated learning model, addressing privacy concerns and regulatory requirements. However, existing FU methods often struggle to balance effective erasure with model utility preservation, especially for class-level unlearning in non-IID settings. We propose Federated Unlearning via Class-aware Representation Transformation (FUCRT), a novel method that achieves unlearning through class-aware representation transformation. FUCRT employs two key components: (1) a transformation class selection strategy to identify optimal forgetting directions, and (2) a transformation alignment technique using dual class-aware contrastive learning to ensure consistent transformations across clients. Extensive experiments on four datasets demonstrate FUCRT's superior performance in terms of erasure guarantee, model utility preservation, and efficiency. FUCRT achieves complete (100\%) erasure of unlearning classes while maintaining or improving performance on remaining classes, outperforming state-of-the-art baselines across both IID and Non-IID settings. Analysis of the representation space reveals FUCRT's ability to effectively merge unlearning class representations with the transformation class from remaining classes, closely mimicking the model retrained from scratch.