Unsupervised blind motion deblurring is still a challenging topic due to the inherent ill-posed properties, and lacking of paired data and accurate quality assessment method. Besides, virtually all the current studies suffer from large chromatic aberration between the latent and original images, which will directly cause the loss of image details. However, how to model and quantify the chromatic aberration appropriately are difficult issues urgent to be solved. In this paper, we propose a general unsupervised color retention network termed CRNet for blind motion deblurring, which can be easily extended to other tasks suffering from chromatic aberration. New concepts of blur offset estimation and adaptive blur correction are introduced, so that more detailed information can be retained to improve the deblurring task. Specifically, CRNet firstly learns a mapping from the blurry image to motion offset, rather than directly from the blurry image to latent image as previous work. With obtained motion offset, an adaptive blur correction operation is then performed on the original blurry image to obtain the latent image, thereby retaining the color information of image to the greatest extent. A new pyramid global blur feature perception module is also designed to further retain the color information and extract more blur information. To assess the color retention ability for image deblurring, we present a new chromatic aberration quantization metric termed Color-Sensitive Error (CSE) in line with human perception, which can be applied to both the cases with/without paired data. Extensive experiments demonstrated the effectiveness of our CRNet for the color retention in unsupervised deblurring.