Magnetic reconnection can occur in current sheets separating magnetic fields sheared by any angle and of arbitrarily different amplitudes. In such asymmetric and non-coplanar systems, it is not yet understood what the orientation of the X-line will be. Studying how this orientation is determined locally by the reconnection process is important to understand systems such as the Earth magnetopause, where reconnection occurs in regions with large differences in upstream plasma and field properties. This study aims at determining what the local X-line orientation is for different upstream magnetic shear angles in an asymmetric set-up relevant to the Earth’s magnetopause. We use two-dimensional hybrid simulations and vary the simulation plane orientation with regard to the fixed magnetic field profile and search for the plane maximizing the reconnection rate. We find that the plane defined by the bisector of upstream fields maximizes the reconnection rate and this appears not to depend on the magnetic shear angle, domain size or upstream plasma and asymmetries.