Context. Medium-resolution échelle spectra of the Red Square Nebula surrounding the star MWC 922 are presented. The spectra have been obtained in 2010 and 2012 using the X-shooter spectrograph mounted on the Very Large Telescope (VLT) in Paranal, Chile. The spectrum covers a wavelength range between 300 nm−2.5 µm and shows that the nebula is rich in emission lines. Aims. We aim to identify the emission lines and use them as a tool to determine the physical and chemical characteristics of the nebula. The emission lines are also used to put constraints on the structure of the nebula and on the nature of the central stars. Results. These findings put constraints on the evolution of the central objects in MWC 922. The Red Square shows strong similarities to the Red Rectangle Nebula, both in morphology and in its mid-IR spectroscopic characteristics. As for the Red Rectangle, the observed morphology of the nebula reflects mass-loss in a binary system. Specifically, we attribute the biconical morphology and the associated rung-like structure to the action of intermittent jets blown by the accreting companion in a dense shell, which has been created by the primary. We stress, though, that despite the morphological similarities, these two objects represent very different classes of stellar objects.