This paper introduces a novel method for subpixel accuracy stabilization of unsteady digital films and video sequences. The proposed method offers a near-closed-form solution to the estimation of the global subpixel displacement between two frames, that causes the misregistration of them. The criterion function used is the mean-squared error over the displaced frames, in which image intensities at subpixel locations are evaluated using bilinear interpolation. The proposed algorithm is both faster and more accurate than the search-based solutions found in the literature. Experimental results demonstrate the superiority of the proposed method to the spatio-temporal differentiation and surface fitting algorithms, as well. Furthermore, the proposed algorithm is designed so that it is insensitive to frame-to-frame intensity variations. It is also possible to estimate any affine motion between two frames by applying the proposed algorithm on three non-collinear points in the unsteady frame.