  We propose a new formulation of the complete tree-level S-matrix of N = 8
supergravity. The new formula for n particles in the k R-charge sector is an
integral over the Grassmannian G(2,n) and uses the Veronese map into G(k,n).
The image of a point in G(2,n) is required to be in the "complement" of a
2|8-plane thus making the SU(8) R-symmetry manifest. The integrand is the ratio
of two determinants. The numerator is an analog of Hodges' recent determinant
formula for MHV amplitudes. The denominator is a 2(n+k-2) x 2(n+k-2) minor of a
2(n+k) x 2(n+k) matrix of rank 2(n+k-2). Just as Hodges' formula does for MHV
amplitudes, our integrand makes the complete invariance under Sn manifest for
all sectors.
  The validity of the new formula follows from two surprising facts. One is the
equivalence of Hodges' MHV formula and the Kawai-Lewellen-Tye (KLT) formula
when kinematic invariants are allowed to be off-shell in a novel way. We give a
proof of this for any number of particles. The second fact is an orthogonality
property of the solutions to the polynomial equations defining the Veronese
embedding. Explicit proof of the orthogonality is given for all amplitudes in
all R-charge sectors with eight or less particles thus providing non-trivial
evidence for our proposal.
