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How to deal with themotion blurred image is a common problem in our daily life. Restoring blurred images is challenging, especially when both the blur kernel and the sharp image are unknown. In this work, we present a new algorithm for removing motion blur from a single image, which incorporates the image decomposition into the image deblurring process. Most of the existing algorithms solving the blind deblurring problem use the alternate iterative mechanism, which alternative estimates the kernel and restores the sharp image. We find that the small gradients of image are not always helpful but sometimes harmful to this kind of iterative algorithm. So we decompose the blurred image into cartoon and texture components. And we only use the cartoon part of the image, which can improve the stability and robustness of the algorithm. Our experiments show that our algorithms can achieve good results in man-made and real-life photos.