Note on the Normalization of Predicted GRB Neutrino Flux

We note that the theoretical prediction of neutrinos from gamma-ray bursts (GRBs) by IceCube overestimates the GRB neutrino flux, because they ignore both the energy dependence of the fraction of proton energy transferred to charged pions and the radiative energy loss of secondary pions and muons when calculating the normalization of the neutrino flux. After correction for these facts the GRB neutrino flux is reduced, e.g., by a factor ~5 for typical GRB spectral parameter, and may be consistent with the present zero event detected by IceCube. More observations are important to push the sensitivity below the prediction and test whether GRBs are the sources of ultra-high energy cosmic rays.