  We present new infinitesimal `conformal-like' symmetries for the field
equations of strictly massless spin-$s \geq 3/2$ totally symmetric
tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime
($dS_{4}$). The corresponding symmetry transformations are generated by the
five closed conformal Killing vectors of $dS_{4}$, but they are not
conventional conformal transformations. We show that the algebra generated by
the ten de Sitter (dS) symmetries and the five conformal-like symmetries closes
on the conformal-like algebra $so(4,2)$ up to gauge transformations of the
gauge potentials. The transformations of the gauge-invariant field strength
tensor-spinors under the conformal-like symmetries are given by the product of
$\gamma^{5}$ times a usual infinitesimal conformal transformation of the field
strengths. Furthermore, we demonstrate that the two sets of physical mode
solutions, corresponding to the two helicities $\pm s$ of the strictly massless
theories, form a direct sum of Unitary Irreducible Representations (UIRs) of
the conformal-like algebra. We also fill a gap in the literature by explaining
how these physical modes form a direct sum of Discrete Series UIRs of the dS
algebra $so(4,1)$.
