Complex generalized basis reduction assisted successive interference cancellation is proposed for mitigating multi-stream interference of transmitted signals in single code Bell Laboratories layered space-time systems. Generalized basis reduction method is modified to better the complex channel matrix, which leads to the extended generalized reduction basis channel matrix with shorter and roughly orthogonal basis vectors in polynomial-time. This distinguished property guarantees the concatenated successive interference cancellation detector, based on the MMSE criterion, converges to the approximately global optimum estimation points. Emulation results have shown that the proposed detection scheme is superior to other suboptimum detection schemes considered in this paper in terms of two points. They are the mitigation of multi-stream interference and the diversity gain. Its performance is close to the sphere decoder but with a lower complexity.