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A dispersive channel in the DS-CDMA downlink destroys the orthogonality of the synchronous users' spreading sequences. In this paper, we aim to reestablish this orthogonality blindly by means of a common chip-level equaliser. The adaptation algorithm is based on a constant modulus criterion forcing the various user symbols onto a constant modulus, for which a stochastic gradient descent algorithm is derived. This algorithm is structurally similar to a multiple error filtered-X LMS type approach, whereby the equaliser input CM update is replaced by a spreading code filtered version. Various simulations demonstrating the algorithm's convergence and noise performance are presented.