The Fluorescence Detector of the Pierre Auger Cosmic Ray Observatory will provide a measurement of the parameters of extensive air showers with energy >10/sup 19/ eV. The mirror of the Fluorescence Detector prototype has dimension /spl sim/3.6/spl times/3.6 m/sup 2/, and is composed of 49 trapezoidal segments of approximately 50/spl times/50 cm/sup 2/. Each segment is curved using a steel mold in which the glass sags in a controlled environment. The glass is then aluminized under vacuum and coated with oxide (Al/sub 2/O/sub 3/). The oxide thickness is chosen to maximize the reflectivity in the wavelength range of fluorescence light (300 nm</spl lambda/<400 nm). The 49 mirror segments, plus eight spare ones, are now ready for installation. The authors discuss the production technique of the segments for the Torino prototype mirror.