The authors continue the study of relationships between Massey products, lower central series of groups and the Fox free differential calculus (cf. their previous paper on the subject [Can. J. Math. 36, 1119-1146 (1984; Zbl 0561.55015)]). In particular, under certain conditions the authors introduce and compute a “universal” Massey product of one- dimensional cohomology classes which has a nice feature of having zero indeterminacy.