A magnetic alternative to the viscous accretion disc, around a non-magnetic star, is presented. The disc field is generated by an αω-dynamo; only weak turbulence is required to produce the α-effect, so the viscous force is negligible. The magnetic force does not significantly affect the vertical equilibrium or the radial momentum, hence stellar gravity balances the thermal pressure gradient vertically and the angular velocity is Keplerian up to a boundary layer close to the stellar surface. The azimuthal magnetic force causes the outward advection of angular momentum necessary for the transfer of matter through the disc at the externally imposed rate. The magnetic field has a quadrupolar structure, soBø is generated by the shearing of radial field. Eigenstate solutions result, the lowest modes corresponding to the lowest temperatures. The values ofBø, in the central plane are ∼ 100 gauss, with essentially vanishing magnetic field at the disc surface.