In this paper, we propose a new decorrelating detector called pseudo-inverse-filtering type decorrelating detector for asynchronous CDMA channels. We first show that the matched filtering and decorrelating operations of the existing decorrelating detectors can be replaced with the pseudo-inverse filtering operations in synchronous channels, and using this fact we show that the decorrelating detector has the largest SNR among the linear detectors that can eliminate MAI. Then we introduce asynchronous pseudo-inverse filtering type decorrelating detector by extending this result for asynchronous channels, and discuss implementation methods of the proposed decorrelating detectors. Since the proposed scheme employs a decentralized structure for updating coefficients, it has the flexibility to add/remove users. Finally we analyze the performance of the proposed decorrelating detector in terms of the bit error rate, and examine its performance improvements over the conventional detectors through computer simulations.