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Summary form only given. For years efforts have been made to understand second harmonic generation (SHG) from the surfaces and interfaces of isotropic metal interfaces. Theoretical and experimental understanding of this process would be helpful for quantitative surface studies based on SHG. However, to our knowledge, there has been no complete measurement of the amplitudes and relative phases of the seven non-zero elements of the second harmonic susceptibility tensor, /spl chi//sup (2)/, for an isotropic metal surface. We report such a measurement of /spl chi//sup (2)/, for air-exposed sputtered Al films. Analysis of the results shows unambiguously that the films are isotropic sources of surface SHG, but also highlight a discrepancy between measurements and the accepted theory.