System identification of civil engineering structures are often formulated as Multiple-Input, Multiple-Output (MIMO) problems due to the complexity of loading conditions such as differential ground motion, which is also multi-directional in nature. Such MIMO system identification problems are challenging due to strong coupling between the contributions of multiple ground motion inputs to each individual response. Compared with Single-Input, Multiple-Output (SIMO) system identification, MIMO problems are often more computationally complex and error prone. In this paper, a new system identification strategy is proposed in which a more complex MIMO problem is converted into a number of SIMO problems by decoupling the contribution of multiple inputs to the outputs. A QR-factorization based approach is adopted for the decoupling and its accuracy is investigated. The effectiveness of the proposed strategy is demonstrated through applications to a two-span straight bridge and a four-span curved bridge, both are highway bridges.