In this letter, the interference cancellation technique is introduced to single carrier (SC) block transmission systems in sparse Rician frequency selective fading channels, and an effective equalizer is presented. Hard decision on the transmitted signal is made by commonly used SC equalizers, and every multipath signal can be constructed by the initial solution and channel state information. Then, final demodulation result is obtained by the line-of-sight component in the received signal which can be achieved by cancelling the other multipath signals in the received signal. The solution can be further used to construct the multipath signals allowing a multistage detector with higher performance to be realized. It is shown by Monte Carlo simulations in an SUI-5 channel that the new scheme offers dramatically higher performance than traditional equalization schemes.