Computer-controlled sub-aperture polishing technology is limited by its propensity to introduce mid-spatial-frequency (MSF) error (ripple error), which significantly inhibits the performance improvement of the optical system. Here, we propose a novel processing form of the magnetorheological finishing (MRF) tool and its generation mechanism. There are specific path angles and steps, with only tens of microns bandwidth (‘magic’ angle step), under which a surface without significant path ripple can be stably realized without affecting the convergence of other frequency errors. The magic angle step is precisely obtained via the scale-variant filtered spectrum analysis. Using the two-dimensional (2-D) Taylor approximation of the tool influence function (TIF), we verify that in the magic angle step state, owing to the shape asymmetry and the edge discontinuity of the TIF, the convolution of TIFs presents a complementary effect. It is first observed in experiments that the MSF error can be abnormally increased by decreasing the path step around the magic angle step state. Therefore, the magic angle step and corresponding analysis model have the potential of being extended to other polishing tools. Furthermore, they can significantly benefit the manufacturing efficiency of high-power laser systems, huge telescopes, and lithography systems, as well as improve existing polishing technologies.