In this paper, we propose OFTv2 to solve the high computational cost and memory usage issues of orthogonal fine-tuning (OFT). Instead of the weight-centric implementation of the traditional OFT, OFTv2 adopts an input-centric approach, which reduces the computational complexity from 3rd order to 2nd order by using matrix-vector multiplication. In addition, we introduce the Cayley-Neumann parameterization, an efficient orthogonal parameterization method to approximate the matrix inverse in the Cayley transform. With these improvements, OFTv2 achieves up to 10x faster training speed and 3x lower GPU memory usage without any performance degradation. In addition, it supports fine-tuning of quantized base models, and demonstrates better training stability, efficiency, and memory usage than QLoRA.