We investigate the nature of the chiral phase transition using the RG improved gauge action and
the Wilson quark action with two degenerate quarks on $32^3\times 16$, $24^3\times 12$, and $16^3\times 8$ lattices.

We introduce RG scaling relations for both the temporal and the spacial effective masses of mesons at
the chiral phase transition point. Numerical results of effective masses at the chiral phase transition on
the three sizes of lattices are excellently on the universal limiting curves for the pseudo-scalar meson
and vector meson, respectively. The scaling enables us to obtain the effective masses in the continuum limit
as functions of the distance.
We also examine the case of massive quarks at the chiral transition. On each size of lattices
a hyper-scaling relations is satisfied and find the anomalous mass dimension $\gamma^{*}\simeq 0.67$--$1.1$.