  We construct certain unstable higher-order homotopy operations indexed by the
simplex categories of $\Delta^{n}$ for ${n\geq 2}$ and prove that all elements
in the homotopy groups of a wedge of spheres are generated under such
operations by Whitehead products and the group structure. This provides a
stronger unstable analogue of Cohen's theorem on the decomposition of stable
homotopy.
