Properties associated with the integrability of the four-dimensional equation of universal hierarchy are considered. In particular, the structure of the algebra of its local symmetries is studied. We show that the second group of exotic cohomologies of this algebra is nontrivial. We prove that the spectral parameter in the well-known covering of this equation is irremovable. A shadow of a nonlocal symmetry was found; using it, we construct the recursion operator. The action of the recursion operator on some local symmetries generates new non-Abelian coverings of the equation.