  We found that the order for the crumpling transition of an intrinsic
curvature model changes depending on the distance between two boundary vertices
fixed on the surface of spherical topology. The model is a curvature one
governed by an intrinsic curvature energy, which is defined on triangulated
surfaces. It was already reported that the model undergoes a first-order
crumpling transition without the boundary conditions on the surface. However,
the dependence of the transition on such boundary condition is yet to be
studied. We have studied in this paper this problem by using the Monte Carlo
simulations on surfaces up to a size N=8412. The first-order transition changes
to a second-order one if the distance increases.
