  We construct an ordered set of commutators in a partially commutative
nilpotent group $F(X; \Gamma; \mathfrak N_m)$. This set allows us to define a
canonical form for each element of $F(X; \Gamma; \mathfrak N_m)$. Namely, we
construct a Maltsev basis for the group $F(X; \Gamma; \mathfrak N_m).$
