  The p_trans-distribution for the diphoton production at the LHC is calculated
in the modified Randall-Sundrum model with a small curvature of the space-time
kappa, and 5-dimensional Planck scale M_5 in the TeV region. The discovery
limits on M_5 are obtained to be 9.4 TeV and 11.6 TeV for the integrated
luminosities 30 fb^(-1) and 100 fb^(-1), respectively. These limits do not
depend on kappa provided it is much smaller than M_5. The account of graviton
widths is a crucial points of our calculations.
