The information-theoretic approach to face recognition is based on the compact coding where face images are decomposed into a small set of basis images. A popular method for the compact coding may be the principal component analysis (PCA) which eigenface methods are based on. PCA based methods exploit only second-order statistical structure of the data, so higher-order statistical dependencies among pixels are not considered. Factorial coding is known as one primary principle for efficient information representation and is closely related to redundancy reduction and independent component analysis (ICA). The factorial code representation exploits high-order statistical structure of the data which contains important information and is expected to give more efficient information representation, compared to eigenface methods. In this paper, we employ the factorial code representation in the reduced feature space found by the PCA and show that the factorial code representation outperforms the eigenface method in the task of face recognition. The high performance of the proposed method is confirmed by simulations.