  We study in detail the trajectories followed by single images during binary
microlensing events. Starting from perturbative resolutions of the lens
equation, we explore the full parameter space by continuity arguments. We see
that the images created during the caustic crossing can recombine with the
others in different ways. This leads to a new classification of the
microlensing events according to the behaviour of the images. We show that the
images involved in these combinations depend on the folds that are crossed at
the entry and at the exit from the caustic. Non-trivial trajectories can be
classified into four main types. Some consequences for the motion of the center
of light of the source in astrometric measurements are also examined.
