Despite tremendous progress achieved in temporal action detection, state-of-the-art methods still suffer from the sharp performance deterioration when localizing the starting and ending temporal action boundaries. Although most methods apply boundary regression paradigm to tackle this problem, we argue that the direct regression lacks detailed enough information to yield accurate temporal boundaries. In this paper, we propose a novel Boundary Likelihood Pinpointing (BLP) network to alleviate this deficiency of boundary regression and improve the localization accuracy. Given a loosely localized search interval that contains an action instance, BLP casts the problem of localizing temporal boundaries as that of assigning probabilities on each equally divided unit of this interval. These generated probabilities provide useful information regarding the boundary location of the action inside this search interval. Based on these probabilities, we introduce a boundary pinpointing paradigm to pinpoint the accurate boundaries under a simple probabilistic framework. Compared with other C3D feature based detectors, extensive experiments demonstrate that BLP significantly improve the localization performance of recent state-of-the-art detectors, and achieve competitive detection mAP on both THUMOS' 14 and ActivityNet datasets, particularly when the evaluation tIoU is high.