  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.
