  Caustic crossing microlensing events provide us a unique opportunity to
measure the relative proper motion of the lens to the source, and so those
caused by binary MACHOs are of great importance for understanding the structure
of the Galactic halo and the nature of MACHOs. The microlensing event
98-SMC-01, occurred in June 1998, is the first event for which the proper
motion is ever measured through the caustic crossing, and this event may be
caused by binary MACHOs as we argue in this Letter. Motivated by the possible
existence of binary MACHOs, we have performed the Monte Carlo simulations of
caustic crossing events by binary MACHOs and investigated the properties and
detectability of the events. Our calculation shows that typical caustic
crossing events have the interval between two caustic crossings ($t_{\rm cc}$)
of about 5 days. We argue that with the current strategy of binary event search
the proper motions of these typical events are not measurable because of the
short time scale. Therefore the proper motion distribution measured from
caustic crossing events suffers significantly from {`}time scale bias{'}, which
is a bias toward finding long time scale events and hence slowly moving lenses.
We predict there are two times more short time scale events ($t_{\rm cc}\le 10$
days) than long time scale events ($t_{\rm cc}\ge 10$ days), and propose an
hourly monitoring observation instead of the nightly monitoring currently
undertaken to detect caustic crossing events by binary MACHOs more efficiently.
