The urgency of predictions in large-t region at LHC stimulated us to present a unified model of small and high t scattering at high energies. Our model is based upon a safe theoretical ground: analyticity, unitarity, Regge behavior, gluon exchange and saturation of bounds established in axiomatic quantum field theory. We make precise predictions for the behavior of the differential cross sections at high t, the evolution of the dip-shoulder structure localized in the region of -t between 0.5 and 0.8 GeV**2 and the radical violation of the exponential behavior of the first diffraction cone at small t.