Failure diagnosis of flowmeters based on control limits has been developed as a method to identify faulty flowmeters, which should be calibrated during a maintenance period, during plant operation. This method is very useful for the diagnosis of flowmeters having faulty errors with magnitudes greater than three times of their control limits. However, there is a shortcoming that the diagnostic results given by this method often miss giving alarms when they should, or give false diagnoses, for faulty errors with magnitudes less than three times of their control limits. In this study, the diagnostic results given by this method during plant operation are not adopted in a straightforward manner. Instead, at least one flowmeter is selected and calibrated during a maintenance period, to identify the true value of a flow rate. As a result, the diagnostic accuracy can be improved by performing a second diagnosis using the calibrated values of the flow rates. Furthermore, the performance of the method presented is demonstrated by numerical experiments on a simplified refinery model containing 11 flowmeters.