  It is shown that high accelerating gradient can be obtained in a specially
constructed system of electron (positron) bunches, moving in cold plasma,with
definite density. These combined bunch systems do not generate the wake fields
behind them and can pass through the plasma column in a periodic sequence. The
consideration is carried out numericaly and analyticaly in one dimensional
approach, (which can be applied to finite system when its transverse dimensions
are larger than plasma wave length, divided by $2\pi$). The possibilities of
the experimental tests by measuring the predicted energy gain are discussed on
the examples of Argonne Wakefield Accelerator and induction linac with typical
parameters.
