We investigate the causal structure of the Harada-Iguchi-Nakao (HIN)'s exac
t solution in detail, which describes the dynamical formation of a naked si
ngularity in the collapse of a regular spherical cluster of counterrotating
particles. There are three kinds of radial null geodesics in the HIN space
time. One is the regular null geodesics and the other two are the null geod
esics which terminate at the singularity. The central massless singularity
is a timelike naked singularity and satisfies the strong curvature conditio
n along the null geodesics except for the instant of singularity formation.
The cluster dynamically asymptotes to the singular static Einstein cluster
in which the centrifugal force is balanced with gravity. The HIN solution
provides an interesting example which demonstrates that collisionless parti
cles invoke a timelike naked singularity.