Group-blind multiuser detectors for uplink code-division multiple-access (CDMA) were recently developed by Wang and Host-Madsen. These detectors make use of the spreading sequences of known users to construct a group constraint to suppress the intracell interference. However, such techniques demand the estimation of the multipath channels and the delays of the known users. In this paper, several improved blind linear detectors are developed for CDMA in fading multipath channels. The proposed detectors utilize the correlation information between consecutively received signals to generate the corresponding group constraint. It is shown that by incorporating this group constraint, the proposed detectors can provide different performance gains in both uplink and downlink environments. Compared with the previously reported group-blind detectors, our new methods only need to estimate the multipath channel of the desired user and do not require the channel estimation of other users. Simulation results demonstrate that the proposed detectors outperform the conventional blind linear multiuser detectors.