A promising design of a КНК-type two-section gas-filled ionization chamber is described for the first time. A relationship between the design parameters, gas pressure, and characteristics of the material is determined, under which full compensation of the background currents from the γ-radiation and the measurement of thermal neutron fluxes in a range of 400 to 7 ×109cm–2s–1at a load characteristic with a ≤ 5% nonlinearity are provided. Test results of the chamber are presented.