  We report the discovery of the second accreting millisecond X-ray pulsar
(AMXP) in the globular cluster NGC 6440. Pulsations with a frequency of 205.89
Hz were detected with the Rossi X-Ray Timing Explorer on August 30th, October
1st and October 28th, 2009, during the decays of ~4 day outbursts of a newly
X-ray transient source in NGC 6440. By studying the Doppler shift of the
pulsation frequency, we find that the system is an ultra-compact binary with an
orbital period of 57.3 minutes and a projected semi-major axis of 6.22
light-milliseconds. Based on the mass function, we estimate a lower limit to
the mass of the companion to be 0.0067 M_sun (assuming a 1.4 M_sun neutron
star). This new pulsar shows the shortest outburst recurrence time among AMXPs
(~1 month). If this behavior does not cease, this AMXP has the potential to be
one of the best sources in which to study how the binary system and the neutron
star spin evolve. Furthermore, the characteristics of this new source indicate
that there might exist a population of AMXPs undergoing weak outbursts which
are undetected by current all-sky X-ray monitors. NGC 6440 is the only globular
cluster to host two known AMXPs, while no AMXPs have been detected in any other
globular cluster.
