Published neoclassical results are misleading as concerns the plasma edge for they do not adequately take the peculiar local conditions into account, in particular the fact that the density and temperature variation length-scales are here quite small: L(N,T) much less than a, R, qR. In the high collisionality regime (qRnu(J)/c(J) much greater than 1), gyro-stress tensor and ion inertia play an essential role if the ratio q2R2/(OMEGA(i)tau(i))aL(N,T) is of order of, or larger than unity. Coupled novel neoclassical equations then obtain, not only for die evolution of the density and temperatures, but also for die radial electric field and the evolution of the parallel ion momentum: gyro-stresses and inertia indeed upset the otherwise de facto ambipolarity of particle transport and a radial electric field necessarily builds up. The increased nonlinear character of these revisited neoclassical equations widens the realm of possible plasma behaviors.