Siberian Federal University

A coordinate system of the 2nd kind is being built, corresponding to canonical coordinates of the 1st kind (terminology A. I. Maltsev), thereby obtaining a parametric solution of the system Lie’s equations. The integral representation of the group operations f(x; y) of the local Lie group G in canonical coordinates 1st kind. As the main apparatus is used modified formula of A.P.Yuzhakov for implicit mappings. The operation f(x; y) is also represented as a power series, which is the reduced form of the series Campbell–Hausdorff