This paper reports the discovery of a bright X-ray transient source, Suzaku J1305-4913, in the south-west arm of the nearby Seyfert II galaxy NGC 4945. It was detected at a 0.5 -- 10 keV flux of $2.2 times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$ during the Suzaku observation conducted on 2006 January 15 -- 17, but was undetectable in a shorter observation on 2005 August 22 --23, with an upper limit of $1.7 times 10^{-14}$ erg cm$^{-2}$ s$^{-1}$ (90% confidence level). At a distance of 3.7 Mpc, the bolometric luminosity of the source becomes $L_{rm bol} = 4.4 times 10^{39} alpha$ erg s$^{-1}$, where $alpha = (cos 60^circ / cos i)$ and $i$ is the disk inclination. Therefore, the source is classified into so-called ultraluminous X-ray sources (ULXs). The time-averaged X-ray spectrum of the source is described by a multi-color disk model, with the innermost accretion disk temperature of $T_{rm in} = 1.69_{-0.05}^{+0.06}$ keV. During the 2006 January observation, it varied by a factor of 2 in intensity, following a clear correlation of $L_{rm bol} propto T_{rm in}^4$. It is inferred that the innermost disk radius $R_{rm in}$ stayed constant at $R_{rm in} = 79_{-3.9}^{+4.0} alpha^{1/2}$ km, suggesting the presence of a standard accretion disk. Relating $R_{rm in}$ with the last stable orbit around a non-rotating black hole yields a rather low black hole mass, $sim 9 alpha^{1/2}$ solar masses, which would imply that the source is shining at a luminosity of $sim3 alpha^{1/2} $ times the Eddington limit. These results can be better interpreted by invoking sub-Eddington emission from a rapidly spinning black hole with a mass of 20 -- 130 solar masses.
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