Here we propose a simple way in which one can considerably improve performance of the gas stripper setup at the GSI UNILAC. To do so, it will be enough to replace inside the main GSI stripper chamber the present nozzle and the short windowless storage gas cell (for pulsed gas-jet operation mode) by a simple conical diverging nozzle combined with a gas catcher tube placed on the axis of gas-jet at some distance downstream the nozzle exit. As a result, the background pressure in the main and differentially pumped adjacent vacuum chambers of the gas stripper at the GSI UNILAC will dramatically reduce, and it will make possible to achieve the required optimal thickness of gas targets. The pulsed gas stripper operation is simply realized by implementing a commercially available fast gas valve connected to the nozzle entrance. Moreover, the ion beam pulses repetition rate can be increased and it will allow for the considerably higher average intensity of the ion beams extracted from the GSI UNILAC. Performance of the proposed GSI UNILAC gas stripper modification we explored by means of detailed computer experiments, which give a realistic description of supersonic gas jets flowing out the nozzle into vacuum. Results of these computer experiments have presented and discussed.