We propose a method for face recognition based on a discriminative linear projection. In this formulation images are treated as tensors, rather than the more conventional vector of pixels. Projections are pursued sequentially and take the form of a rank one tensor, i.e., a tensor which is the outer product of a set of vectors. A novel and effective technique is proposed to ensure that the rank one tensor projections are orthogonal to one another. These constraints on the tensor projections provide a strong inductive bias and result in better generalization on small training sets. Our work is related to spectrum methods, which achieve orthogonal rank one projections by pursuing consecutive projections in the complement space of previous projections. Although this may be meaningful for applications such as reconstruction, it is less meaningful for pursuing discriminant projections. Our new scheme iteratively solves an eigenvalue problem with orthogonality constraints on one dimension, and solves unconstrained eigenvalue problems on the other dimensions. Experiments demonstrate that on small and medium sized face recognition datasets, this approach outperforms previous embedding methods. On large face datasets this approach achieves results comparable with the best, often using fewer discriminant projections.