This paper presents an algorithm to characterize scattering parameters of multi-port device with a four-port Vector Network Analyzer (VNA). By employing the renormalization of scattering matrices with different reference impedances at ports, data obtained from multi-port configuration measurements can be synthesized to build the full scattering matrix of the device-under-test (DUT). Although that procedure can be best used for the interconnect system in which the inside routing is quite apparent, we still need an appropriate algorithm to select specific S-parameters for the black-box model where the configuration inside is not known. This paper presents an algorithm to determine which S-parameters are suitable to be selected to reconstruct the full S-matrix of the system. Using the selected specific S-parameters, the renormalization of the scattering matrices could be synthesized to successfully estimate the S-parameters of a multiport interconnect system. A good agreement between the estimated and true S-parameters verifies the validness of the algorithm.