This paper proposes a new method called MoRA for parameter-efficient fine-tuning of large language models (LLMs). The proposed method, MoRA, employs a square matrix to achieve high-rank updating, maintaining the same number of trainable parameters. The paper suggests that low-rank updating, as implemented in LoRA, may limit the ability of LLMs to effectively learn and memorize new knowledge. MoRA outperforms LoRA on memory-intensive tasks and achieves comparable performance on other tasks.