The Campbell-Hausdorff formula gives rise to an element .
Different choices lead to elements of which belong to the same U - orbit.
The author shows that, if the number of double points of a marked singular link L is large enough, then there is a choice of a Milnor system for each resolution of singularities such that the usual signed sum vanishes. His construction of such an uniform choice involves a marking, i.e. a distinguished point on each component of L away from the double points. This may be used to convert L into a singular string link , by cutting along a disk D in which intersects L transversally at the marked points. This is due to the fact that the former can easily detect changes of orientation, while the latter cannot detect the non-invertibility of links.