Monitor of All sky X-ray Image (MAXI) discovered a new outburst of an X-ray transient source named MAXI J1421-613. Because of the detection of three X-ray bursts from the source, it was identified as a neutron star low-mass X-ray binary. The results of data analyses of the MAXI GSC and the Swift XRT follow-up observations suggest that the spectral hardness remained unchanged during the first two weeks of the outburst. All the XRT spectra in the 0.5-10 keV band can be well explained by thermal Comptonization of multi-color disk blackbody emission. The photon index of the Comptonized component is $approx$ 2, which is typical of low-mass X-ray binaries in the low/hard state. Since X-ray bursts have a maximum peak luminosity, it is possible to estimate the (maximum) distance from its observed peak flux. The peak flux of the second X-ray burst, which was observed by the GSC, is about 5 photons cm$^{-2}$ s$^{-1}$. By assuming a blackbody spectrum of 2.5 keV, the maximum distance to the source is estimated as 7 kpc. The position of this source is contained by the large error regions of two bright X-ray sources detected with Orbiting Solar Observatory-7 (OSO-7) in 1970s. Besides this, no past activities at the XRT position are reported in the literature. If MAXI J1421-613 is the same source as (one of) them, the outburst observed with MAXI may have occurred after the quiescence of 30-40 years.
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