  We propose a new type of gauge-invariant expansion of the ionization
probability amplitudes of atoms by short pulses of electromagnetic radiation.
Contrary to previous gauge-invariant approaches to this problem it does not
require different partitions of the total Hamiltonian depending on the choice
of gauge. In a natural way the atomic potential is treated as perturbation
acting on an electron interacting with strong pulse. Whereas this is a standard
assumption of strong field approximation (SFA), we show that grouping
consequently together \textit{all} terms of the same order in the atomic
potential results in the expansion of the amplitude which is gauge invariant
\textit{order by order}, and not only in the limit of infinite series. In this
approach, which is illustrated by numerical examples, the "direct ionization"
and "rescattering" contributions are different from those commonly used in SFA
- calculations.
