  We present a study of collisionless magnetic reconnection within the
framework of full two-fluid MHD for a completely ionized hydrogen plasma,
retaining the effects of the Hall current, electron pressure and electron
inertia. We performed 2.5D simulations using a pseudo-spectral code with no
dissipative effects. We check that the ideal invariants of the problem are
conserved down to round-off errors. Our results show that the change in the
topology of the magnetic field lines is exclusively due to the presence of
electron inertia. The computed reconnection rates remain a fair fraction of the
Alfv\'en velocity, which therefore qualifies as fast reconnection.
