The class of switching networks, composed of stages of identical square switches arranged symmetrically around a center stage (Benes' networks), is considered. The synthesis problem of selecting from this class a rearrangeable network with the minimum number of crosspoints is solved. Benes' approach, (using relation of covering), is taken into consideration. The new structures of the networks are in some cases different than those already known. Modifications of Benes' theorems result in lowering the number of stages of a switching network with the minimum number of crosspoints. This lowering can bear some practical significance, which could simplify the control devices. A model comparison is given of the known and new results.