ISP (Image Signal Processor) serves as a pipeline converting unprocessed raw images to sRGB images, positioned before nearly all visual tasks. Due to the varying spectral sensitivities of cameras, raw images captured by different cameras exist in different color spaces, making it challenging to deploy ISP across cameras with consistent performance. To address this challenge, it is intuitively to incorporate a raw-to-raw mapping (mapping raw images across camera color spaces) module into the ISP. However, the lack of paired data (i.e., images of the same scene captured by different cameras) makes it difficult to train a raw-to-raw model using supervised learning methods. In this paper, we aim to achieve ISP generalization by proposing the first unsupervised raw-to-raw model. To be specific, we propose a CSTPP (Color Space Transformation Parameters Predictor) module to predict the space transformation parameters in a patch-wise manner, which can accurately perform color space transformation and flexibly manage complex lighting conditions. Additionally, we design a CycleGAN-style training framework to realize unsupervised learning, overcoming the deficiency of paired data. Our proposed unsupervised model achieved performance comparable to that of the state-of-the-art semi-supervised method in raw-to-raw task. Furthermore, to assess its ability to generalize the ISP model across different cameras, we for the first formulated cross-camera ISP task and demonstrated the performance of our method through extensive experiments. The codes are released at https://github.com/ydxxxx/Unsupervised-Raw-to-raw-Mapping.