We report on 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 RXTE on 2009 August 30, October 1 and October 28, during the decays of lsim4 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 semimajor axis of 6.22 lt-ms. 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.