The existing theory for alongshore rhythmic bars relies on morphodynamic instabilities involving the wave-driven longshore current and rip currents. Transverse finger bars are common on coasts with a beach profile above the equilibrium profile (something not related to those currents). Here we show that under these conditions, the cross-shore transport can induce an instability which is triggered by the onshore transport together with wave refraction by the emerging bars. It is a finite amplitude instability, something not previously found in coastal geomorphology. We use a numerical model that filters out the dynamics associated to those currents. The alongshore spacing scales with the wavelength of the incident waves and the cross-shore extent is about the distance from shore to the depth of closure. The modelled bars compare qualitatively well with observations at El Trabucador back-barrier beach (Ebro delta, Western Mediterranean Sea).