Direct numerical simulations of decaying two‐dimensional magnetohydrodynamic flows at Reynolds numbers of several thousand are performed, using resolutions of 10242collocation points. An inertial range extending to about one decade is observed, with spectral properties depending on the velocity–magnetic field correlation. At very small scales, resistive tearing destabilizes current sheets generated by the inertial dynamics and leads to the formation of small‐scale magnetic islands, which may then grow and reach the size of inertial scales.