We investigate experimentally the "mean free path" of electrons injected selectively into the outer spin-polarized edge channel of the lowest Landau level. A simple model allows us to determine the characteristic length between two spin-flip scattering events directly from the measured resistance plateaus. Typical spin-flip equilibration lengths between 100 ìm and 1 mm are found. The size of the observed equilibration lengths is interpreted in terms of the spin-orbit interaction, which also leads to a local g-factor enhancement at the edge.