  We present morphological analyses of Post-starburst galaxies (PSBs) at
$0.7<z<0.9$ in the COSMOS field. We fitted ultraviolet to mid-infrared
multi-band photometry of objects with $i<24$ from COSMOS2020 catalogue with
population synthesis models assuming non-parametric, piece-wise constant
function of star formation history, and selected 94 those galaxies that have
high specific star formation rates (SSFRs) of more than $10^{-9.5}$ yr$^{-1}$
in 321--1000 Myr before observation and an order of magnitude lower SSFRs
within recent 321 Myr. We devised a new non-parametric morphological index
which quantifies concentration of asymmetric features, $C_{A}$, and measured it
as well as concentration $C$ and asymmetry $A$ on the Hubble Space
Telescope/Advanced Camera for Surveys $I_{\rm F814W}$-band images. While
relatively high $C$ and low $A$ values of PSBs are similar with those of
quiescent galaxies rather than star-forming galaxies, we found that PSBs show
systematically higher values of $C_{A}$ than both quiescent and star-forming
galaxies; 36% of PSBs have $\log{C_{A}} > 0.8$, while only 16% (2%) of
quiescent (star-forming) galaxies show such high $C_{A}$ values. Those PSBs
with high $C_{A}$ have relatively low overall asymmetry of $A \sim 0.1$, but
show remarkable asymmetric features near the centre. The fraction of those PSBs
with high $C_{A}$ increases with increasing SSFR in 321--1000 Myr before
observation rather than residual on-going star formation. These results and
their high surface stellar mass densities suggest that those galaxies
experienced a nuclear starburst in the recent past, and processes that cause
such starbursts could lead to the quenching of star formation through rapid gas
consumption, supernova/AGN feedback, and so on.
