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This paper proposes an angular invariant feature for registration procedure to perform reliable matching between two similarity 3D protein structures. The feature is defined by a k- dimensional vector with k angles between the normal vector of each point and its k-nearest-neighbors individually. The feature is invariant to scale transformation, rotation transformation. We present that an angular augment coefficient should be set to avoid rounding error of computer. This new invariant feature makes defect detection of 3D protein structures, faster and more robust.