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Bayesian nonlocal (NL) (BNL) means filter, as an extension of the NL means algorithm, provides a general framework for image denoising when dealing with different noise. However, this approach makes a strong assumption that image patch itself provides a good approximation on the true parameter, which leads to the bias problem particularly under serious speckle noise. Another disadvantage of the BNL filter is that the commonly used patch preselection method cannot effectively exclude the outliers. In this letter, a new form of the BNL filter is presented for the purpose of synthetic aperture radar image despeckling, which incorporates the technique of sigma filter to cope with the bias problem. In addition, pixel preselection is adopted based on the refined sigma range, which greatly contributes to the preservation of the image details such as edges, texture, and the strong reflective scatters. Experimental results illustrate that the proposed BNL filter reaches the state-of-the-art performance on both the visual quality and evaluation indexes.