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In an earlier paper \cite{yu2021Finiteness}, we showed that there arefinitely many stationary configurations (consisting of equilibria, rigidlytranslating configurations, relative equilibria and collapse configurations) inthe planar four-vortex problem. However, we only established finiteness ofcollapse configurations in the sense of prescribing a  collapse constant. In this paper, by developing ideas of Albouy-Kaloshin andHampton-Moeckel to do an analysis of the singularities, we further show thatthere really are finitely many collapse configurations in the four-vortexproblem. This is an unexpectedly result, because the $N$-vortex problem hasinfinitely many collapse configurations for $N= 3$ and for $N= 5$. %to completethe work on finiteness of stationary configurations of the planar four-vortexproblem.  We also provide better upper bounds for collapse configurations than that in\cite{yu2021Finiteness}.

Finiteness of Stationary Configurations of the Planar Four-vortex Problem. II