Most research on nonorthogonal space-time block codes (NO-STBC) assumes that channel state is quasistatic (slow fading). However, time-selective (fast fading) channels do exist in practice. In that case, the existing NO-STBC detector described in Hamid Jafarkhani (2001) can suffer from an irreducible error floor. To this end, this paper proposes an interference cancellation (IC) signal detector. While the computational complexity of the IC detector is a little higher than that of the conventional detector, the new IC detector provides better performance by subtracting the interference resulting from the fast fading channels. Meanwhile, we also offer an improved IC detector, which can obtain much lower bit error rates (BER) at the cost of a further complexity increase, based on the nonorthogonal property of the codes.