Foundation models have achieved tremendous success in different domains. However, their huge computation and storage complexity make these models difficult to fine-tune and also less applicable in practice. Recent study shows training in Fourier domain can be an effective fine-tuning method in terms of both model performance and number of training parameters. In this work, we propose to further reduce the complexity by the factorization through the product of interleaved circulant and diagonal matrices. In addition, we address the case of non-square fine-tuning weights by partitioning the circulant matrix into blocks. Our method avoids the construction of weight change matrix and utilizes 1D fast Fourier transform (FFT) instead of 2D FFT. Experimental results show that our method achieves similar or better performance across various tasks with much less floating-point operations (FLOPs) and the number of trainable parameters.