In this paper it is shown numerically that axially-symmetric solutions of the Navier-Stokes equations, which describe the rotating flow above a disk which is itself rotating, are non-unique. The numerical techniques designed to calculate such solutions with a high power of resolution are given. Especially the behaviour in and around the first branching point is considered. It is found that fors=−0.16054 two branches coincide. The second branch has been almost completely calculated. It ranges back to positive values ofs.