  In another article we associated a dynamical system to a non-properly ordered
Bratteli diagram. In this article we describe how to compute the $K-$group
$K_0$ of the dynamical system in terms of the Bratteli diagram. In the case of
properly ordered Bratteli diagrams this description coincides with what is
already known, namely the so-called dimension group of the Bratteli diagram.
The new ordered group defined here is more relevant for non-properly ordered
Bratteli diagrams. We use our main result to describe $K_0$ of a substitutional
system.
