  We study celestial amplitudes in (super) Yang-Mills theory using a
parameterisation of the spinor helicity variables where their overall phase is
not fixed by the little group action. In this approach the spin constraint
$h-\bar{h}=J$ for celestial conformal primaries emerges naturally from a new
Mellin transform, and the action of conformal transformations on celestial
amplitudes is derived. Applying this approach to $\mathcal{N}\!=\!4$ super
Yang-Mills, we show how the appropriate definition of on-shell superspace
coordinates leads naturally to a formulation of chiral celestial
superamplitudes and a representation of the generators of the four-dimensional
superconformal algebra on the celestial sphere, which by construction
annihilate all tree-level celestial superamplitudes.
