This paper presents an extension of previous methods in order to find electrical series-connections between multiphase machines allowing the independent control of each one of them. These new electrical series-connections explore the symmetrical disposition of the phases of even-multiphase machines, allowing the inversed connection of some of the phases, different from the direct connections as it was previously done. Therefore, electrical series-connections of two symmetrical 6- phase or of four symmetrical 10-phase machines are now possible. Besides that, this new solution ensures a natural independent control of permanent magnet synchronous machines even if the back-electromotive forces generated by the rotor are not sinusoidal, without need of special machine conception or supplementary control strategy. This control independency is mathematically proved using the decomposition of multiphase machines in fictitious diphase and homopolar machines. Experimental results are presented to show the functioning and the advantages of this new coupling for two symmetrical 6-phase permanent magnet synchronous machines.