A method to define the complex structure and separate the conformal mo
de is proposed for a surface constructed by two-dimensional dynamical
triangulation. Applications are made for surfaces coupled to matter fi
elds such as n scalar fields (n = 0, 1 and 4) and m Ising spins (m = 1
and 3). We observe a well-defined complex structure for cases when th
e matter central charges are less than and equal to one, while it beco
mes unstable beyond c = 1. This can be regarded as the transition expe
cted in analytic theories.