  We give a simple proof of the Curtis' theorem: if $A_\bullet$ is
$k$-connected free simplicial abelian group, then $L^n(A_\bullet)$ is an $k+
\lceil \log_2 n \rceil$-connected simplicial abelian group, where $L^n$ is the
functor of $n$-th Lie power. In the proof we do not use Curtis' decomposition
of Lie powers. Instead of this we use the Chevalley-Eilenberg complex for the
free Lie algebra.
