The transport of high-energy runaway electrons near the outside of a low-density ORMAK discharge is investigated by measuring the flux of runaways to the outer limiter during and after an inward shift of the plasma column. The experimental results are interpreted through a runaway confinement model which includes both the classical outward displacement of the runaway orbit with increasing energy and an additional runaway spatial diffusion coefficient which simulates an unspecified source of anomalous transport. Diffusion coefficients in the range D ≅ 102–104 cm · s−1 are found under various discharge conditions indicatinga significant non-collisional runaway transport near the outside of the discharge, particularly in the presence of MHD instability.