Image descriptors are widely adopted structures to match image features. SIFT-based descriptors are collections of gradient orientation histograms computed on different feature regions, commonly divided by using a regular Cartesian grid or a log-polar grid. In order to achieve rotation invariance, feature patches have to be generally rotated in the direction of the dominant gradient orientation. In this paper we present a modification of the GLOH descriptor, a SIFT-based descriptor based on a log-polar grid, which avoids to rotate the feature patch before computing the descriptor since predefined discrete orientations can be easily derived by shifting the descriptor vector. The proposed descriptors, called sGLOH and sGLOH+, have been compared with the SIFT descriptor on the Oxford image dataset, with good results which point out its robustness and stability.