In this paper, a new feature extraction algorithm considering both two-directional two-dimensional principal component analysis ((2D)²PCA) and independent component analysis (ICA), called (2D)²PCA-ICA, is proposed for face representation. This algorithm analyzes the principal components of image vectors on 2D matrices by simultaneously considering the row and column directions as opposed to the standard PCA based on 1D vectors, and transforming those principal components to the independent components that maximize the non-Gaussianity of the sources. These two major techniques such as (2D)²PCA and ICA are used sequentially in order to obtain the most efficient features that properly describe a whole set of human faces in face databases. The proposed algorithm is applied to the face recognition problem. Simulation results on ORL and Yale B face databases shows that the proposed algorithm achieves high average success rate in face recognition compared with other models.