  Generalizing the work of Sen, we analyze special points in the moduli space
of the compactification of the F-theory on elliptically fibered Calabi-Yau
threefolds where the coupling remains constant. These contain points where they
can be realized as orbifolds of six torus $T^6$ by $Z_m \times Z_n (m, n=2, 3,
4, 6)$. At various types of intersection points of singularities, we find that
the enhancement of gauge symmetries arises from the intersection of two kinds
of singularities. We also argue that when we take the Hirzebruch surface as a
base for the Calabi- Yau threefold, the condition for constant coupling
corresponds to the case where the point like instantons coalesce, giving rise
to enhanced gauge group of $Sp(k)$.
