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