In this work, we propose a new image rotation algorithm. The main feature of our approach is the symmetric reversibility, which means that when using the same algorithm for the converse operation, then the initial data is recovered exactly. To that purpose, we decompose the lattice conversion process into three successive shear operations. The translations along the shear directions are implemented by 1-D convolutions, with new appropriate fractional delay filters. Also, the method is fast and provides high-quality resampled images.