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This paper presents a blind adaptive decorrelating detector for asynchronous multicarrier code-division multiple-access (MC-CDMA) systems with Rayleigh-fading channels. This detector is derived by making use of the cross-correlation matrix between the consecutively received signals. The main attraction of the detection algorithm is its simplicity, since the detector can be implemented blindly without channel estimation, except for the synchronization of the desired user. To implement the proposed detector, a new adaptive subspace-tracking algorithm for any Hamiltonian matrices is developed, while the previously reported subspace-tracking methods can only estimate the subspace of a positive Hamiltonian matrix. Since a common drawback of the multiuser detector based on the subspace method is the existence of a phase factor that usually deteriorates the performance of the detector, a new method is developed to compensate for the phase of the proposed detector, based on the property of the complex white Gaussian noise. Results of extensive computer simulations show the performance improvement of the proposed detector.