In this paper, a new type of optical vortex called the squared Laguerre–Gauss (LG)2 vortex beam has been investigated. Theoretical conclusions and numerical experiment confirm that these beams are Fourier-invariant and retain their structure at the focus of a spherical lens. In the Fresnel diffraction zone, such a beam is transformed into a superposition of conventional LG beams, the number of which is equal to the number of rings in the (LG)2 beam. The presented beams are structurally stable in the case of one intensity ring.