  It is numerically shown that the discontinuous character of the helicity
modulus of the two-dimensional XY model at the Kosterlitz-Thouless (KT)
transition can be directly related to a higher order derivative of the free
energy without presuming any {\it a priori} knowledge of the nature of the
transition. It is also suggested that this higher order derivative is of
intrinsic interest in that it gives an additional characteristics of the KT
transition which might be associated with a universal number akin to the
universal value of the helicity modulus at the critical temperature.
