Detection of the best symmetry plane in 3D images can be treated as a registration problem between the original and the reflected images. The registration is performed in 3D space of parameters defining orientation and shift of reflection plane. We use the normalized l₂ metric as the similarity measure between original and reflected images and investigate an algorithm for computation of the best symmetry plane. The algorithm computes first an initial position of the plane by analyzing principal inertia axes. We demonstrate on several MR brain images that the initial position is in the neighborhood of the global maximum. Therefore the downhill simplex method is further used for the computation of the best symmetry plane. The proposed algorithm was tested on simulated and real MR brain images.