The non-maximum suppression (NMS) is widely used in frame-based tasks as an essential post-processing algorithm. However, event-based NMS either has high computational complexity or leads to frequent discontinuities. As a result, the performance of event-based corner detectors is limited. This paper proposes a general-purpose asynchronous non-maximum suppression pipeline (ANMS), and applies it to corner event detection. The proposed pipeline extract fine feature stream from the output of original detectors and adapts to the speed of motion. The ANMS runs directly on the asynchronous event stream with extremely low latency, which hardly affects the speed of original detectors. Additionally, we evaluate the DAVIS-based ground-truth labeling method to fill the gap between frame and event. Evaluation on public dataset indicates that the proposed ANMS pipeline significantly improves the performance of three classical asynchronous detectors with negligible latency. More importantly, the proposed ANMS framework is a natural extension of NMS, which is applicable to other asynchronous scoring tasks for event cameras.