Based on the BiCR algorithm, s-BiCR algorithm is proposed to solve nonsymmetric linear systems. Firstly, the basic computation frame for the s-BiCR was given by introducing the fundamental principle in the new method and the solution approach to the parameters. Next, according to the analysis of the characters of the sequences of residual vectors and direction vectors, an approach is deduced to reduce computational volume for the parameters so that a more effective advanceds-BiCR is designed. Finally, the correctness ofs-BiCR is proved, that is, the ith approximate solution froms-BiCR is equal to the isth approximate solution from BiCR. In addition, by performance analysis, the number of both synchronous communication and accessing memory fors-BiCR is less than the one for BiCR so the algorithm here has better parallel feature and data locality. The effectivity and validity ofs-BiCR have been confirmed by experiments.