We report a new measurement of the momentum spectra of both positive and ne
gative muons as a function of atmospheric depth in the momentum range 0.3-2
and 0.3-40 GeV/c, respectively. The measured flux values have been compare
d with the spectra obtained from simulations, which were carried out to int
erpret the atmospheric neutrino data. We find that our data disagree with t
he results from the simulations. The ratio of the flux of muons derived fro
m simulations to that measured is at largest 1.8 and varies with atmospheri
c depth and muon momentum.