We construct a new X-ray (2--10 keV) luminosity function of Compton-thin active galactic nuclei (AGNs) in the local universe, using the first MAXI/GSC source catalog surveyed in the 4--10 keV band. The sample consists of 37 non-blazar AGNs at $z=0.002-0.2$, whose identification is highly ($>97%$) complete. We confirm the trend that the fraction of absorbed AGNs with $N_{rm H} > 10^{22}$ cm$^{-2}$ rapidly decreases against luminosity ($L_{rm X}$), from 0.73$pm$0.25 at $L_{rm X} = 10^{42-43.5}$ erg s$^{-1}$ to 0.12$pm0.09$ at $L_{rm X} = 10^{43.5-45.5}$ erg s$^{-1}$. The obtained luminosity function is well fitted with a smoothly connected double power-law model whose indices are $gamma_1 = 0.84$ (fixed) and $gamma_2 = 2.0pm0.2$ below and above the break luminosity, $L_{*} = 10^{43.3pm0.4}$ ergs s$^{-1}$, respectively. While the result of the MAXI/GSC agrees well with that of HEAO-1 at $L_{rm X} gtsim 10^{43.5}$ erg s$^{-1}$, it gives a larger number density at the lower luminosity range. Comparison between our luminosity function in the 2--10 keV band and that in the 14--195 keV band obtained from the Swift/BAT survey indicates that the averaged broad band spectra in the 2--200 keV band should depend on luminosity, approximated by $Gammasim1.7$ for $L_{rm X} ltsim 10^{44}$ erg s$^{-1}$ while $Gammasim 2.0$ for $L_{rm X} gtsim 10^{44}$ erg s$^{-1}$. This trend is confirmed by the correlation between the luminosities in the 2--10 keV and 14--195 keV bands in our sample. We argue that there is no contradiction in the luminosity functions between above and below 10 keV once this effect is taken into account.
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