Summary: A novel blind adaptive multiuser detection scheme, the linear decorrelating detector (LDD), based on the concept of complementary subspace is proposed. Under this scheme, the information bits can be estimated from the received signal with the prior knowledge of the desired user's signature waveform and its timing. The technique has two key elements: a geometric notion of the LDD and the subspace-based concept to estimate the orthogonal complement of the interfering space. It is then shown that the LDD can be formulated in terms of the interference space constructed from the received signal and the desired user's signature waveform. The interference space components can be adaptively estimated using the modified power-based methods with only \(O((K - 1) N)\) flops of computation at each iteration, where \(N\) is the processing gain and \(K\) is the number of active users in the channel. It is seen that compared with the previous subspace-based blind adaptive detector [\textit{K. S. Gilhousen}, \textit{I. M. Jakobs}, \textit{R. Padovani}, \textit{A. J. Viterbi}, \textit{L. A. Weaver} and \textit{C. E. Wheatley}, ``On the capacity of a cellular CDMA system'', IEEE Trans. Veh. Technol. 40, 303-311 (1991)], having a computational complexity of \(O(KN)\) per iteration, our novel blind adaptive detector offers lower computational complexity. The proposed blind multiuser detection offers the optimal near-far resistance, low computational complexity, and resistance against the orthogonality error of the estimated interference space.