A recombination chamber is proposed to be for determination of ambient dose equivalent, H*(10) during high-altitude flights and space missions. Polarising electrodes of the chamber are supplied from two capacitors permanently connected to the electrodes. Ions, collected on the measuring electrode, charge a measuring capacitor that is also permanently connected to the electrode. The collected charge is proportional to H*(10), so the chamber with only three capacitors creates a whole measuring system. The special procedure was introduced for charging the supplying capacitors and for reading the voltage on the measuring capacitor. The procedure has to be performed in laboratory conditions before and after the flight. The measuring system with recombination chamber of REM-2 type allows to measure the H*(10) above 10 µSv with uncertainly ca. 25% in any field of penetration radiation, with an integration time up to some days. The system has been checked in field conditions.