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Traditional equalization algorithms for multiple input multiple output (MIMO) systems suffer from high complexity and low convergence rate. So it's necessary to develop an equalization algorithm to minimize the computational complexity and improve the convergence rate. This paper presents a new adaptive reduced-rank linear equalization algorithm, called rectangle unitary multistage Wiener filter reduced-rank equalization (RUMSWFRE). In the equalization process, the rectangle blocking matrix is utilized by multistage Wiener filter and implemented by the correlation subtraction algorithm. The new scheme uses a rectangle blocking matrix, which is chosen from the square blocking matrix of unitary multistage Wiener filter (UMSWF). And it can reduce the size of observation data vectors step by step in the forward recursion decomposition of UMSWF. In this way, the computational complexity is reduced and the convergence rate becomes faster. Performance analysis and simulation results show that this proposed method yields similar error performance with much lower computational complexity and faster convergence rate compared with the traditional ones.