Synthetic aperture radar (SAR) images are corrupted by speckle noise, which degrades the quality and interpretation of the images. Speckle removal provides a better interpretability of SAR images if the technique performs the filtering without loss of spatial resolution and preserves fine details and edges. This work aims to redefine the neighborhood areas around the noisy pixel and in this area the local mean and variance are computed to estimate the Maximum a Posteriori (MAP) filter parameters. The proposed modified MAP algorithm improves the ability to filter the speckle noise without blurring edges and targets by applying the MAP estimator in the current adaptive window that is controlled by a measure of homogeneity in the area around the noisy pixel. This adaptive windowing was also incorporated to the classical Kuan et al. (1985) and Frost et al. (1982) filters in order to evaluate the performance of the proposed scheme. The effectiveness in reducing speckle by the modified MAP filter is evaluated in terms of qualitative and quantitative aspects such as line and edge preservation and the improvement of the signal to noise ratio. The tests were performed in real SAR images.