Most left-handed metamaterials cannot be described by local effective permittivity or permeability tensors in the visible or near-infrared due to the mesoscopic size of the respective unit cells and the related strong spatial dispersion. We lift this problem and propose a metamaterial exhibiting artificial magnetism that does not suffer from this restriction. The artificial magnetism arises from the extreme coupling between both metallic films forming the unit cell. We show that its electromagnetic response can be properly described by biaxial local constitutive relations. A genuine biaxial left-handed fishnet metamaterial is suggested, which can be realized by atomic layer deposition to fabricate the nanoscaled spacing layers required for extreme coupling.