Abstract: Human face is a complex biomechanical system and non-linearity is a remarkable feature of facial expressions. However, in blendshape animation, facial expression space is linearized by regarding linear relationship between blending weights and deformed face geometry. This results in the loss of reality in facial animation. To synthesize more realistic facial animation, aforementioned relationship should be non-linear to allow the greatest generality and fidelity of facial expressions. Unfortunately, few existing works pay attention to the topic about how to measure the non-linear relationship. In this paper, we propose an optimization scheme that automatically explores the non-linear relationship of blendshape facial animation from captured facial expressions. Experiments show that the explored non-linear relationship is consistent with the non-linearity of facial expressions soundly and is able to synthesize more realistic facial animation than the linear one.