  We revisit the constraint on the maximum mass of cold spherical neutron stars
coming from the observational results of GW170817. We develop a new framework
for the analysis by employing both energy and angular momentum conservation
laws as well as solid results of latest numerical-relativity simulations and of
neutron stars in equilibrium. The new analysis shows that the maximum mass of
cold spherical neutron stars can be only weakly constrained as $M_{\rm max}
\alt 2.3M_\odot$. Our present result illustrates that the merger remnant
neutron star at the onset of collapse to a black hole is not necessarily
rapidly rotating and shows that we have to take into account the angular
momentum conservation law to impose the constraint on the maximum mass of
neutron stars.
