This paper presents a novel second-order output spectrum (SOOS) based method to diagnose multiple bolt loosening faults in structures with a sensor chain. This new method is based on a recently-developed nth-order output spectrum estimation (nth-OSE) algorithm using only proper input-output data measured from a chain of sensors. The properties of the SOOS transmissibility of the sensor chain along physical structures are studied systematically. In the new method, the noise effect on accuracy of the estimation of fault indicators is investigated as well. The new method also considers more general nonlinear restoring forces not only due to faults but also caused by inherent nonlinearity in structure when deriving the properties of the SOOS transmissibility. Extensive simulation results demonstrate that the SOOS of the studied structure can be estimated efficiently, and the SOOS transmissibility can be used as an effective and reliable damage indicator for the detection and location of multiple bolt loosening faults in structures.