  We study the non-wandering set of $C^3$ contracting Lorenz maps $f$ with
negative Schwarzian derivative. We show that if $f$ doesn't have attracting
periodic orbit, then there is a unique topological attractor. Precisely, there
is a transitive compact set $\Lambda$ such that $\omega_f(x)=\Lambda$ for a
residual set of points $x \in [0,1]$. We also develop in the context of Lorenz
maps the classical theory of spectral decomposition constructed for Axiom A
maps by Smale.
