In this paper, a method is proposed for the design of a non-negatively interactive FACTS-based stabilizer in a multi-machine power system. It is demonstrated in the paper that the FACTS-based stabilizer can be designed to impose positive interactions upon other stabilizers in the power system through the correct selection of non-negatively interactive installing locations and feedback signals of the FACTS-based stabilizer and the proper setting of the phase angle of the FACTS-based stabilizer. An example power system is presented in the paper, where a TCSC-based stabilizer is designed, which is not only able to damp the target inter-area oscillation mode effectively but also imposes a positive interaction with a PSS in the power system to damp a local oscillation mode.