The purpose of this paper is to present a radically new image transform, called the Minimax Eigenvector Decomposition (MED) transform. This novel transform is based on the minimax product of two matrices and is an analogue of the Singular Value Decomposition (SVD) transform of linear algebra. In comparison to the SVD transform, in the MED transform eigenvalues need not be computed as they turn out to be zero. Furthermore, computation of eigenvectors is trivial. This makes the use of the MED transform more desirable as the major problem associated with the SVD transform is the computation of the singular values and eigenvectors. These are computationally extensive and often lead to significant numerical errors.