  Let $\CV$ be a vector field distribution on manifold $M$. We give an
efficient algorithm for the construction of local coordinates on $M$ such that
$\CV$ may be locally expressed as some partial prolongation of the contact
distribution $\Cal C^{(1)}_q$, on the first order jet bundle of maps from $\Bbb
R$ to $\Bbb R^q$, $q\geq 1$. It is proven that if $\CV$ is locally equivalent
to a partial prolongation of $\Cal C^{(1)}_q$ then the explicit construction of
contact coordinates algorithmically depends upon the determination of certain
first integrals in a sequence of geometrically defined and algorithmically
determined integrable Pfaffian systems on $M$. The number of these first
integrals that must be computed satisfies a natural minimality criterion. These
results therefore provide a full and constructive generalisation of the
classical Goursat normal form from the theory of exterior differential systems.
