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To effectively preserve the edges of a synthetic aperture radar (SAR) image when despeckling, an algorithm with edge detection and fuzzy clustering in the translation-invariant second-generation bandelet transform (TIBT) domain is proposed in this letter. A Canny operator is first utilized to detect and remove edges from the SAR image. Then, TIBT and fuzzy C-mean clustering are employed to decompose and despeckle the edge-removed image, respectively. Finally, the removed edges are added to the reconstructed image. The algorithm suggests each coefficient in high-frequency subbands as the clustering feature, proposes a calculation method of the best clustering number, and defines the signal and noise in the clustering results. Experimental results show that the visual quality and evaluation indexes outperform the other methods with no edge preservation. The proposed algorithm effectively realizes both despeckling and edge preservation and reaches the state-of-the-art performance.