The complexity of electronic systems for RF and digital applications is ever increasing, and the corresponding compliance analysis for ensuring the required specifications in terms of performances, signal and power integrity is a challenging task often accomplished by relying on commercial circuit simulators. The modeling of multiport devices involves the assembly of electrical networks usually described in terms of S-parameter. This work proposes a new single-step algorithm that computes the global S-parameter matrix for a cascade of multiple networks with multiple ports without the need of any S-parameter transformation in T-parameters and their inverse transformation. The proposed method involves the construction of a large matrix filled with all S-parameters of all networks, and the subsequent evaluation of only one matrix expression. The proposed method is shown to be very efficient and reliable, since it can be easily automated without the need of a manual connections of tens or even hundreds of ports of the multiple blocks, which is an action that needs to be performed within a typical circuit simulator environment. Also, the proposed method overcomes the limitation of the standard method based on S-to-T parameter transformation since it is of general applicability to networks with different number of input and output ports. Examples involving the cascade of multiple 2-ports and multiports networks are considered, and the results are validated and compared with the reference results obtained from a commercial circuit simulator. The proposed method is shown to be effective and fast compared to its counterpart based on the T-parameters.