Ionization of atomic systems by strong and short laser pulses is considered in a new gauge invariant version of the Strong
Field Approximation (SFA). The standard version of SFA (SSFA), which is usually applied to the theoretical description
of interaction with strong laser fields, is dependent on the choice of gauge of the vector potential describing the laser
radiation. Theoretical predictions of SSFA may differ significantly depending on the choice of gauge. In particular,
substantial differences have been observed in the case of two most frequently used length and velocity gauges. Gauge
invariant expression for the ionization amplitude was obtained by grouping consequently all terms which are of the same
order in atomic potential, treated as a perturbation compared to strength of the coupling with external laser field.
Contrary to previous gauge-invariant formulations the present approach does not require different gauge-dependent
partitions of the Hamiltonian. Preliminary tests of the present approach applied to ionization of Hydrogen atom show
qualitative agreement with results obtained by solving numerically Time Dependent Schrödinger Equation (TDSE).