This paper introduces UoRA, a novel parameter-efficient fine-tuning (PEFT) approach for large language models (LLMs). UoRA achieves state-of-the-art efficiency by leveraging a low-rank approximation method that reduces the number of trainable parameters without compromising performance. Unlike existing methods such as LoRA and VeRA, UoRA employs a re-parametrization mechanism that eliminates the need to adapt frozen projection matrices while maintaining shared projection layers across the model. This results in halving the trainable parameters compared to LoRA and outperforming VeRA in computation and storage efficiency. Comprehensive experiments across various benchmarks demonstrate UoRA’s superiority in achieving competitive fine-tuning performance with minimal computational overhead. We demonstrate its performance on GLUE and E2E benchmarks and is effectiveness in instruction-tuning large language models and image classification models. Our contributions establish a new paradigm for scalable and resource-efficient fine-tuning of LLMs.