  A puzzle in the iron-based superconductor LaFeAsO_{1-x}F_x is that the
magnetic moment obtained by first-principle electronic structure calculations
is unexpectedly much larger than the experimentally observed one. For example,
the calculated value is ~ 2.0 \mu_B in the mother compound, while it is ~ 0.3
\mu_B in experiments. We find that the puzzle is solved within the framework
LDA + U by expanding the U value into a slightly negative range. We show U
dependence of the obtained magnetic moment in both the undoped x=0.0 and doped
x = 0.125. These results reveal that the magnetic moment is drastically reduced
when entering to the slightly negative range of U. Moreover, the negative U
well explains other measurement data, e.g., lattice constants and electronic
DOS at the Fermi level. We discuss possible origins of the negative U in these
compounds.
