The full operator method (FOM) has been proposed to overcome some of the shortcomings of the commonly used operator splitting method (OSM). In particular, the FOM is improved by increasing the accuracy of both the predictor and corrector using the estimated tangent stiffness of the tested structure. The numerical characteristics of the FOM, including stability and accuracy, are investigated in this study. It is shown that FOM is conditionally stable. The stability and accuracy characteristics are dependent on the accuracy of the estimated tangent stiffness and the parameters associated with the acceleration variation in the time-stepping integration method. Mass-spring systems with different types of nonlinearity, including hardening, stiffening, and softening behavior, are used to evaluate the performance of the FOM. It is found that the FOM can capture these types of nonlinearity with satisfactory accuracy. Using a prototype 12-story composite coupled wall system, the influences of the strong nonlinearity of the system as well as the displacement control errors from hydraulic actuators on the performance of the FOM are explored. The results show that the FOM is capable of generating reasonably accurate results despite the presence of strong structural nonlinearity and displacement control errors. The full operator method (FOM) has been proposed to overcome some of the shortcomings of the commonly used operator splitting method (OSM). In particular, the FOM is improved by increasing the accuracy of both the predictor and corrector using the estimated tangent stiffness of the stability of the FOM, including stability and accuracy, are investigated in this study. It is shown that FOM is conditionally stable. The stability and accuracy characteristics are dependent on the accuracy of the estimated tangent stiffness and the parameters associated with the acceleration variation in the time-stepping integration method. Mass-spring systems with different types of nonlinearity, including hardening, stiffening, and softening behavior, are used to evaluate the performance of the FOM. It is found that the FOM can capture these types of nonlinearity with satisfactory accuracy. Using a prototype 12-story composite coupled wall system, the influences of t he strong nonlinearity of the system as well as the displacement control errors from hydraulic actuators on the performance of the FOM are explored. The results show that the FOM is capable of generating reason reasonably accurate despite despite the presence of strong structural nonlinearity and displacement control errors.