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A new degradation model of motion blurred images by considering so-called "boundary effects" is presented in the paper. It is the existence of the boundary effects that make the methods based on old models invalid. The new model reveals that the real part and imaginary part of the degraded image spectra at some special frequency points keep their signs almost unchanged in the sense of statistics. Fortunately, this characteristic can be used to estimate the degraded parameter. Also, we can decrease the sensitivity of the method to noise by choosing the subimages properly.