A steady-state two-dimensional model of the outermost region of a spiral galaxy is presented. The magnetic field, which is able to explain the flat rotation curve, is calculated, without the existence of any kind of dark matter. The vertical and radial distributions of the density are calculated, as well as the radial and vertical velocities. The magnetic field strength is noticeably constant in the peripheral disc, at about 7x10(-7) gauss, much more moderate than that obtained in our previous model (Battaner et al.). The vertical velocities are driven by Parker's instabilities and induce a moderate escape of gas of about 0.1 M. yr(-1) which prevents excessive flaring.