A measurement of the Cs spin-exchange cross section (σex = 1.40 ± 0.10 × 10−14 cm2) is presented. It is a result of an experiment on the hyperfine relaxation of an optically pumped cesium vapor in the presence of nitrogen buffer gas in experimental conditions which ensure the absence of quadrupole contributions and the minimizing of the influence of high diffusion orders on the relaxation signals.