  An exact solution for a high speed deterministic traffic model with open
boundaries and synchronous update rule is presented. Because of the strong
correlations in the model, the qualitative structure of the stationary state
can be described for general values of the maximum speed. It is shown in the
case of $v_{\rm max}=2$ that a detailed analysis of this structure leads to an
exact solution. Explicit expressions for the stationary state probabilities are
given in terms of products of $24\times 24$ matrices. From this solution an
exact expression for the correlation length is derived.
