Abstract: Recent methods for facial landmark location perform well on close-to-frontal faces but have problems in generalising to large head rotations. In order to address this issue we propose a second order linear regression method that is both compact and robust against strong rotations. We provide a closed form solution, making the method fast to train. We test the method’s performance on two challenging datasets. The first has been intensely used by the community. The second has been specially generated from a well known 3D face dataset. It is considerably more challenging, including a high diversity of rotations and more samples than any other existing public dataset. The proposed method is compared against state-of-the-art approaches, including RCPR, CGPRT, LBF, CFSS, and GSDM. Results upon both datasets show that the proposed method offers state-of-the-art performance on near frontal view data, improves state-of-the-art methods on more challenging head rotation problems and keeps a compact model size.