An unsupervised change-detection method specifically oriented to improve the change-detection accuracy of synthetic aperture radar (SAR) images is proposed. This method has four main steps. First, a preprocessing method is proposed based on the Kalman filter. We concentrate on reducing the false detection or missing detection rate caused by only using a single filter. Second, the difference image containing explicit information about the changed region is generated based on a standard log-ratio operator. Third, an improved nonsubsampled shearlet transform (NSST) algorithm based on the nonlocal means (NLM) filter is proposed. Simultaneously, we decompose the difference image into low-frequency and high-frequency subbands by the improved NSST algorithm. In particular, in order to effectively preserve the detailed information while denoising, the NLM filter is used to suppress the noise of the high-frequency subbands. Fourth, the final difference image is obtained by the fuzzy C-means algorithm, which is selected because of its high clustering performance and wide range of applications. Experiments conducted on three real datasets of images demonstrate the effectiveness of the proposed method.