  We classify C$^*$ near-group categories by using Vaughan Jones theory of
subfactors and the Cuntz algebra endomorphisms. Our results show that there is
a sharp contrast between two essentially different cases, integral and
irrational cases. When the dimension of the unique non-invertible object is an
integer, we obtain a complete classification list, and it turns out that such
categories are always group theoretical. When it is irrational, we obtain
explicit polynomial equations whose solutions completely classify the C$^*$
near-group categories in this class.
