The detection of significant local reflectional symmetry in grey level images is considered. Prior segmentation is not assumed, and it is intended that the results could be used for guiding visual attention and for providing side information to segmentation algorithms. A local measure of reflectional symmetry that transforms the symmetry detection problem to a global optimization problem is defined. Reflectional symmetry detection becomes equivalent to finding the global maximum of a complicated multimodal function parameterized by the location of the center of the supporting region, its size, and the orientation of the symmetry axis. Unlike previous approaches, time consuming exhaustive search is avoided. A global optimization algorithm for solving the problem is presented. It is related to genetic algorithms and to adaptive random search techniques. The efficiency of the suggested algorithm is experimentally demonstrated. Just one thousand evaluations of the local symmetry measure are typically needed in order to locate the dominant symmetry in natural test images.