  We are interested in the structure of the Lcc vertex in the Yang-Mills
theory, where c is the ghost field and L the corresponding BRST auxiliary
field. This vertex can give us information on other vertices, and the possible
conformal structure of the theory should be reflected in the structure of this
vertex. There are five two-loop contributions to the Lcc vertex in the
Yang-Mills theory. We present here calculation of the first of the five
contributions. The calculation has been performed in the position space. One
main feature of the result is that it does not depend on any scale, ultraviolet
or infrared. The result is expressed in terms of logarithms and Davydychev
integral J(1,1,1) that are functions of the ratios of the intervals between
points of effective fields in the position space. To perform the calculation we
apply Gegenbauer polynomial technique and uniqueness method.
