In this paper, we propose a novel shape descriptor that is robust in differentiating intrinsic symmetric points on geometric surfaces. Our motivation is that even the state-of-theart shape descriptors and non-rigid surface matching algorithms suffer from symmetry flips. They cannot differentiate surface points that are symmetric or near symmetric. Hence a left hand of one human model may be matched to a right hand of another. Our Symmetry Robust Descriptor (SRD) is based on a signed angle field, which can be calculated from the gradient fields of the harmonic fields of two point pairs. Experiments show that the proposed shape descriptor SRD results in much less symmetry flips compared to alternative methods. We further incorporate SRD into a stand-alone algorithm to minimize symmetry flips in finding sparse shape correspondences. SRD can also be used to augment other modern non-rigid shape matching algorithms with ease to alleviate symmetry confusions.