A new version of the J-matrix method is formulated for describing the (e; 2e) and (e; 3e) scattering of a fast projectile electron on a helium atom. The derived three-body final state wave function exactly satisfies two-body boundary conditions when one ejected electron is at large distances from while the other is close to the nucleus. The obtained results for differential cross sections of the He(e; 2e)He⁺ and He(e; 3e)He⁺⁺ reactions are in a good agreement with experiment both in shape and absolute value.