For multicarrier code-division multiple access (MC-CDMA) systems employing Alamouti's simple space-time block coding (STBC), a special relationship between two minimum mean-square error (MMSE) filter weight vectors is derived in which one filter is for detecting odd-indexed symbols and the other for even-indexed symbols. Using this relationship, a modified MSE cost function is presented and an improved least mean-square (LMS) adaptive receiver is proposed. Since the number of filter taps independently updated in the proposed adaptive receiver is only half that of the conventional LMS adaptive receiver, the proposed adaptive receiver has a faster convergence rate than the conventional LMS adaptive receiver while keeping the same steady-state MSE performance. This is verified through the simulation.