In this letter, we propose a novel method to extract illumination-invariant features for face recognition and verification under varying illuminations. Inspired by the fact that normalized coefficients of the singular value decomposition (SVD) are insensitive to different illumination conditions, we exploit a simple, yet powerful scheme for describing underlying structures of faces, so-called SVD face. In contrast to previous approaches still suffering from the loss of details, our SVD face greatly preserves textures of the original image based on the relaxation of SVD coefficients. Theoretical analysis shows that our SVD face is an illumination-invariant measure and has an ability to discover meaningful components (e.g., eyes, mouth, etc.) of face images while suppressing the effect of various illuminations. Experimental results on both Yale B and our illuminated face (IF) datasets demonstrate that the SVD face is effective for face recognition and verification compared to previous approaches proposed in literature.