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The radon exhalation rate from the medium surface is commonly derived using a scheme involving a radon detector and an accumulation chamber. The accumulation chamber accumulates the radon gas to make its concentration level inside the chamber detectable by the radon detector in the scheme. The common calculation method for deriving the exhalation rate is based on an assumption that the radon concentrations in the detector's internal cell and that in the accumulation chamber become equal with sufficient accumulation time. However, based on our recent experiments, this method tends to underestimate the actual exhalation rates as generated by our simulation facility. To correct this, we develop a new method for computing the exhalation rate based on the non-equilibrium concept. This paper presents the new method.