One-hour-averaged fluxes of 1.8- to 2.15-MeV protons observed by the LET2 detector on Pioneer 10 on the inbound trajectory showed anisotropies attributable to corotation of Jupiter's magnetodisc only when Pioneer was near the dipole equator. Most of the time the anisotropy greatly exceeded the value expected from corotation. Gradients in the distribution function can be used to account for this excess anisotropy, but the amount of gradient required is unacceptably large by 1--2 orders of magnitude. If they were taken as real, these gradients would predict almost complete disappearance of these protons from Jupiter's magnetosphere in a matter of hours. The remedy is to introduce into the model of the distribution function proton flow along field lines away from the equator into both the southern and the northern hemisphere. The parallel flux at the southernmost latitudes reached by Pioneer can reach 25% of the product of proton density and velocity, i.e., 25% of the maximum possible.