For a previously proposed measurement system for the permeability of wood panels, I have modified the system so that an arbitrary pressure below atmospheric pressure can be applied to both ends of the measurement specimen. The repeatedly measured flow rate of a non-permeable material using this measurement system showed a very small variation under some specific pressure conditions. Assuming that the measurement result of the non-permeable material was the leakage amount of the measurement system, an equation was determined to estimate the leakage amount of the measurement system as a function of the differential pressure between the both ends of the specimen. By subtracting this equation from the measurement results of each sample, I found that the permeability can be determined even for extremely low permeability samples that could not be measured before. This is expected to be useful for research on the gas permeability of wood materials.