In row projection methods, such as Block-Cimmino, the linear dependency between partitions inﬂuence the spectrum of the iteration matrix. In this talk we show our approach to break the linear dependency possible such as the spectrum is clustered around the value 1. The idea is to permute the matrix such as the partitions are interconnected only with their neighbours. Next, we extend the matrix such as the partitions in the resulting superspace are mutually orthogonal to each other making the eigenvalues equal to 1. We present aslo a less restrictive approach that keeps the advantages of the method.