We are aiming to detect local deceleration of Japanese spontaneous conversational speech. We have proposed the variable threshold (VT), which detects local speech rate deceleration from the sequence of time series of mora duration. In this paper, we add a constant term to the VT to detect local deceleration appropriately. The VT is applied to 167 samples of Japanese spontaneous speech taken from a spoken dialogue corpus. The results of the detection are compared with local decelerations which are perceived by a listener. The VT detects 64 phrases among whole 87 decelerated phrases. We confirm the reduction of the incorrect detection of non-decelerated portions by adding a constant term to the VT.