  We report on the X-ray properties of the new transient Swift J0840.7$-$3516,
discovered with Swift/BAT in 2020 February, using extensive data of Swift,
MAXI, NICER, and NuSTAR. The source flux increased for $\sim 10^3$ s after the
discovery, decayed rapidly over $\sim$ 5 orders of magnitude in 5 days, and
then remained almost constant over 9 months. Large-amplitude short-term
variations on time scales of 1--$10^4$ s were observed throughout the decay. In
the initial flux rise, the source showed a hard power-law shaped spectrum with
a photon index of $\sim 1.0$ extending up to $\sim 30$ keV, above which an
exponential cutoff was present. The photon index increased in the following
rapid decay and became $\sim 2$ at the end of the decay. A spectral absorption
feature at 3--4 keV was detected in the decay. It is not straightforward to
explain all the observed properties by any known class of X-ray sources. We
discuss the possible nature of the source, including a Galactic low mass X-ray
binary with multiple extreme properties and a tidal disruption event by a
supermassive black hole or a Galactic neutron star.
