Reflection symmetry is a very commonly occurring feature in both natural and man-made objects, which helps in understanding objects better and makes them visually pleasing. Detection of reflection symmetry is a fundamental problem in the field of computer vision and computer graphics which aids in understanding and representing reflective symmetric objects. In this work, we attempt the problem of detecting the 3D global reflection symmetry of a 3D object represented as a point cloud. The main challenge is to handle outliers, missing parts, and perturbations from the perfect reflection symmetry. We propose a descriptor-free approach, in which, we pose the problem of reflection symmetry detection as an optimization problem and provide a closed-form solution. We show that the proposed method achieves state-of-the-art performance on the standard dataset. © 2020 Elsevier Ltd