We report the measurement of the fragmentation cross sections in high-energy nucleus-nucleus collisions using the 158 A GeV P b 82+ beam from the CERN-SPS. The fragments have charges changed from that of the incident projectile nucleus by ∆Z = Z P b − Z f rag , with 8 ≤ ∆Z < 75. The targets range from polyethylene to lead. Charge identification is made with CR39 nuclear track detectors, measured with an automatic image analyzer system. The measured fragmentation cross sections are parameterized with an empirical relation in terms of the atomic mass of the target, and of the charge of the final fragment.PACS numbers: 25.70.Mn,29.40.Wk