An infinite-dimensional non-Abelian superalgebra is constructed, denoted as shsa(1), which gives rise at the linearized level to linearized curvatures of both massless and auxiliary fields, suggested previously by one of us (M.V.). Various properties of shsa(1) are analysed in detail. Specifically, subalgebras of shsa(1) are found which pretend themselves for the role of independent superalgebras of higher spins and auxiliary fields. A simple operator realization of shsa(1) is presented. P-reversal automorphisms are constructed. N=2 anti-de Sitter superalgebra osp(2, 4) is shown to be a maximal finite-dimensional subalgebra of shsa(1)/o(2). It is observed that the even (boson) subalgebra of shsa(1) decomposes into the direct sum of two infinite-dimensional Lie algebras each giving rise to massless fields of all integer spins. Possible physical implications of this fact are discussed briefly.