An efficient measurement methodology is proposed to construct the scattering parameters of a multi-port device using a four-port vector network analyzer (VNA) without the external un-terminated ports. By using the four-port VNA, the reflected waves from the un-terminated ports could be minimized. The proposed method significantly enhances the accuracy of the S-parameters with less number of measurements compared to the results of classical renormalization technique which uses two-port VNA. The proposed method is validated from the measured data with the coupled 8-port micro-strip lines.