Global 3D point cloud registration has been solved by finding putative matches between the point clouds for establishing alignment hypotheses. A naive approach would try to perform exhaustive search of triplets with a cubic runtime complexity in the number of data points. Super4PCS reduces this complexity to linear by making use of sets of 4 coplanar points. This paper proposes 2-Point-Normal Sets (2PNS), a new global 3D registration approach that advances Super4PCS by using 2 points and their normals for generating alignment hypotheses. The dramatic improvement in the complexity of 2PNS when compared to Super4PCS is demonstrated by the experiments that show speed-ups of two orders of magnitude in noise-free datasets and up to 5.2× in Kinect scans, while improving robustness and alignment accuracy, even in datasets with overlaps as low as 5%.