A constrained minimum mean square error (CMMSE)-RAKE receiver for multipath fading channels is developed by extending the CMMSE receiver for flat fading channels. Based on the observation that interpath interference causes a bias of the channel estimator in [8], a receiver that can remove such a bias is proposed, plus a closed-form expression of the bit-error rate of the receiver is derived. Computer simulation is used to demonstrate that the proposed receiver can outperform existing RAKE receivers.