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Modifications to the first phase of Neiman's algorithm to control the rearrangeable switching networks (RSN) are presented. This algorithm is not limited to networks composed of (2 × 2 )switches. These modifications result in lowering the upper bound on the number of iterative steps which must be performed in the second phase of Neiman's algorithm. An example is given to show that this bound is tight. With RSN's of base 2 structure, the modified Neiman's algorithm is seen to be equivalent to the looping algorithm previously studied. It is also pointed out that the interpretation of the control for RSN as a matrix decomposition can have some practical significance which could increase the efficiency in switch rearrangements. The modified algorithm was implemented with a minicomputer, and a typical printout appears in the Appendix.