  We show that every continuous and dually translation invariant valuation on
the space of Lipschitz functions on the unit sphere of $\mathbb{R}^n$, $n\ge2$,
can be decomposed uniquely into a sum of homogeneous valuations of degree $0$,
$1$ and $2$. In particular, there does not exist any non-trivial, continuous
and dually translation invariant valuation which is homogeneous of degree $3$
or higher. For the space of those of degree $0$, $1$ and $2$ we provide a
description of a dense subspace.
