In this paper, we propose an interference canceller for asynchronous DS-CDMA. The principle is based on parallel cancellation using soft decision(PCSD), however, we propose to add an operation to suppress the strength of interfering signals replica on PCSD. We show here that this operation plays a very important theoretical role in PCSD, and that the performance of our proposed scheme approaches that of a perfect decorrelating detector under certain conditions. With this theoretical background in mind, we named this scheme the "Near-Decorrelating Multistage Detector"(NDMD). To demonstrate NDMD performance, we performed two kinds of computer simulations. In the first kind of simulation, simple conditions are assumed in order to evaluate basic cancelling performance. In the other kind of simulation, essential techniques for CDMA cellular systems such as FEC, transmission power control(TPC), and base band filtering were implemented while taking into account NDMD as applied to such systems. These simulations numerically demonstrate that NDMD is very efficient in cancelling out interference and that it improves asynchronous DS-CDMA performance.