It has been known that if the local Poincare map is quadratic and ther
e are no external noises, the characteristic relation of type-I interm
ittency is of the form epsilon-1/2. However, we here show that various
characteristic relations such as -ln epsilon and epsilon(-nu)(0 less-
than-or-equal-to nu less-than-or-equal-to 1/2) appear according to rei
njection probability distributions.