  In this paper we study the {\it {achromatic arboricity}} of the complete
graph. This parameter arises from the arboricity of a graph as the achromatic
index arises from the chromatic index. The achromatic arboricity of a graph
$G$, denoted by $A_{\alpha}(G)$, is the maximum number of colors that can be
used to color the edges of $G$ such that every color class induces a forest but
any two color classes contain a cycle. In particular, if $G$ is a complete
graph we prove that \[\frac{1}{4}n^{\frac{3}{2}}-\Theta(n) \leq
A_{\alpha}(G)\leq \frac{1}{\sqrt{2}}n^{\frac{3}{2}}-\Theta(n).\]
