A blind multi-user detection algorithm for space-time block coded (STBC) signals is proposed based upon subspace methods and constant modulus algorithms for multiple antenna based receivers. The subspace method is used to determine blindly the multiuser detector required for the mitigation of multi-user interference and to coherently combine multipath and multiple receive antenna signals. It is shown that this subspace method for STBC could however, solve this problem only up to a matrix ambiguity and the structure of this ambiguity matrix looks like a channel matrix obtained for a Single user STBC system with frequency non-selective channel. Hence, the remaining problem is shown to be equivalent to blind equalisation of a single user STBC in flat fading channels. A tap constrained constant modulus algorithm is proposed to solve the remaining problem. In this blind method, only the signature waveform of the user of interest is assumed to be known, and the signature waveforms of all other users in addition to the channel impulse responses of all the users are assumed to be unknown. Simulation results confirm Superior performance of the proposed method over conventional non-blind matched filters.