Taming the Non Abelian Born-Infeld Action

We show how to reduce the non abelian Born-Infeld action describing the interaction of two D-particles to the sum of elliptic integrals depending on simple kinematic invariants. This representation gives explicitly all alpha' corrections to D-particle dynamics. The alpha' corrections induce a stabilization of the classical trajectories such as the ``eikonal'' which are unstable within the Yang-Mills approximation.