A model for a spin-1/2 ladder system with two legs is introduced. It is dem
onstrated that this model is solvable via the Bethe ansatz method for arbit
rary values of the rung coupling J. This is achieved by a suitable mapping
from the Hubbard model with appropriate twisted boundary conditions. We det
ermine that a phase transition between gapped and gapless spin excitations
occurs at the critical value J(c) = 1/2 of the rung coupling.