KLT and New Relations for N=8 SUGRA and N=4 SYM

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In this short note, we prove the supersymmetric Kawai-Lewellen-Tye (KLT) relations between N=8 supergravity (SUGRA) and N=4 super Yang-Mills (SYM) tree-level amplitudes in the frame of S-matrix program, especially we do not use string theory or the explicit Lagrangian form of corresponding theories. Our supersymmetric KLT relations naturally unify the non-supersymmetric KLT relations and newly discovered gauge theory identities and produce more identities for amplitudes involving scalars and fermions. We point out also that these newly discovered identities can be used to reduce helicity basis from (n-3)! further down.