In order to be able to match correctly the track elements produced by a muon in the Tracker and the Muon System of the CMS experiment [1] the mutual alignment precision between the Tracker and the Barrel Muon System must be no worse than 100-400 micrometers depending on the radial distance of the muon chambers from the Tracker. To fulfill this requirement an alignment system had to be designed. This system contains subsystems for determining the positions of the barrel and endcap chambers while a third one connects these two to the Tracker. Since the Barrel muon chambers are embedded into the magnet yoke of the experiment a nonconventional alignment method had to be developed. In this paper we restrict ourselves to the Barrel Alignment System and the calibration methods of its components
