We present a novel reconstruction method for the appearance-based gaze estimation that allows inferring persons' gaze under natural head movement. We first study that the locally linear combination in the respective manifolds consisting of stable left and right eye appearances is efficient. The local structure of the manifolds is destroyed when there is head movement. This is due to the destruction of the intrinsic relations between the two eyes(left and right) when we do locally linear combinations. We then introduce a new combination of both eye appearances, which maintains the relation embedding into the reconstruction of the training stage. Through comparison with other well known methods, we show that the proposed method achieves an optimal performance with head pose variation.