  In this paper we suggest an {\it iterative} algorithm to compute
automatically the scattering matrix elements of any given effective lagrangian,
$\Gamma$. By exploiting the relation between $\Gamma$ and the connected Green
function generator, $Z$, we provide a formula which does not require the use of
the Feynman graphs and it is suitable to implement a numerical routine. By
means of this algorithm we have built a relatively simple and fast fortran code
which we have used to calculate, at the tree level, the rate of four fermion
production at LEP I\negthinspace{I} (finding a very good agreement with
previous calculation) with and without the emission of one observable photon.
