The PETRA IV project will have a storage ring with an ultra-low natural emittance of 20 pm rad. For an off-axis injection scheme with working points at the difference resonance, it is critical to ensure that the vertical excursion caused by transversal coupling does not affect injection efficiency. In this contribution, we present simulation results of an off-axis injection near the coupling resonance, which provides equal equilibrium emittances. The advantages and disadvantages of such a scheme are discussed.