We consider the problem of the relative motion both of the substructures of the Local Group of galaxies (revealed via the S-tree method), and of the velocity of the Local Group itself. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via a 3D reconstruction procedure, which uses information on the radial velocities of the galaxies but does not take account of their distances. Once the bulk motion of the substructures is estimated we also consider, in combination with the observed cosmic microwave background (CMB) dipole, the mean velocity of the Local Group itself. Assigning to the Local Group the mean motion of its main substructures, we evaluate its peculiar velocity in Milky Way frame V_LG-->MW=(-7+/-303, -15+/-155, +177+/-144) or 178 km s^-1 toward galactic coordinates l=245 and b=+85. Combined with the CMB dipole V_MW-->CMB, we obtain a Local Group velocity in CMB frame: V_LG-->CMB=(-41+/-303, -497+/-155, 445+/-144) or 668 km s^-1 towards l=265 and b=42. This estimation is in good agreement, within the 1sigma level, with the estimation of Yahil et al.