Abstract The effect of moving holes in a Hubbard model close to half filling is considered as far as it affects the magnetic order in a superconducting ground state. Starting from an effective Hamiltonian it is argued that, in the low hole-density limit, the problem can be formulated in terms of a spin Hamiltonian including both nearest neighbor and three site antiferromagnetic couplings, the latter originating in the motion of carriers. This term leads to frustration of the Ne´el antiferromagnetic ground state and destroys it for a critical hole concentration. Instead an RVB type state is stabilized as is seen from calculations on finite size systems. These conclusions are also supported by calculations in which the disordered state is represented in terms of a classical Coulomb gas following Kalmeyer and Laughlin.