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In this paper we derive higher derivative corrections to the elevendimensional supergravity by applying the Noether method with respect to the N=1local supersymmetry. An ansatz for the higher derivative effective action,which includes quartic terms of the Riemann tensor, is parametrized by 132parameters. Then we show that by the requirement of the local supersymmetry,the higher derivative effective action is essentially described by twoparameters. The bosonic parts of these two superinvariants completely matchwith the known results obtained by the perturbative calculations in the typeIIA superstring theory. Since the calculations are long and systematic, webuild the computer programming to check the cancellation of the variationsunder the local supersymmetry. This is an extended version of our previouspaper hep-th/0508204.Comment: 67 pages, no figure, references added, typos correcte

Higher derivative corrections to eleven dimensional supergravity via local supersymmetry