Oppopnent-color mechanism in the retinal ganglion cell carries the luminance-chrominance transform important to human vision. Though a variety of opponent-color spaces have been proposed, the orthonormality and the achromatic grayness in the basis function are not always guaranteed. This paper discusses a foundation of complete opponent-color space based on the concept of FCS (Fundamental Color Space) derived from Matrix-R theory. A complete opponent-color space is constructed by [1] choosing the Golden Vectors as an orthogonal triplet for FCS, [2] replacing its luminance basis by the fundamental of EE spectrum, and [3] orthonormalizing the basis functions with GramSchmidt method. The fundamental of EE spectrum is bimodal-shaped. This distinct basis makes the mathematical completeness in the opponent-color FCS possible. So far, the Golden Vectors with fundamentals for (λ₁=455, λ₂ =513, λ₃=584 nm) by J. B Cohen is known to give an ideal orthogonal triplet, but is not an optimal set. The author found a new set of Golden Vectors with the fundamentals for (λ₁=461, λ₂=548, λ₃=617 nm) as the best. A complete opponent-color FCS satisfying both orthonormality and chromatic graynesss is derived from this new Golden Vectors. The paper shows how the proposed opponent-color FCS works well to separate the opponent-color components for natural images and introduces an application to the image color segmentation.