We carry out Monte Carlo simulations of a semi-flexible chain model, in whi
ch we add a bending and torsional restrictions to the bead-spring model. Fr
om our simulations for various temperatures, we show that the coil and glob
ule state coexist over a finite temperature region for stiff chains. On the
basis of our analysis, we assert that the ratio of the persistence length
to the chain length is a key factor in determining whether or not the coexi
stence of the two states appears for short chains. This assertion of ours d
iffers from the proposition offered by the so-called modern theory of coil-
globule transitions which argues that the persistence length itself is a de
ciding factor.