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Muon identification (MUID) and high-momentum measurement accuracy is crucial to fully exploit the physics potential that will be accessible with the ATLAS experiment at the LHC. The muon energy of physics interest ranges in a large interval from few GeV, where the b-physics studies dominate the physics program, up to the highest values that could indicate the presence of new physics. The muon detection system of the ATLAS detector is characterized by two high-precision tracking systems, namely the inner detector (ID) and the muon spectrometer, (MS) plus a thick calorimeter that ensures a safe hadron absorption filtering with high-purity muons with energy above 3 GeV. In order to combine the muon tracks reconstructed in the ID and the MS, a MUID object-oriented software package has been developed. The purpose of the MUID procedure is to associate tracks found in the MS with the corresponding ID track and calorimeter information in order to identify muons at their production vertex with optimum parameter resolution. The performance of these two combined systems has been evaluated with Monte Carlo studies using single muons of fixed-transverse momentum and with full physics events.