In general face classification problems, only the internal features of the face are commonly used, rejecting the information located at head, chin, and ears, since due to their variability is not easy to extract this information. In this paper, a complete scheme based on a Top-Down reconstruction algorithm to extract External Features of face images is proposed. We use the Non negative Matrix Factorization (NMF) algorithm to obtain the final coefficients that encode the external information and using this codification the faces are classified. Our experimental results in different face classification problems show that the information contributed by the external features is significant and useful for classification purposes.