This note investigates the problem of global output feedback stabilization for a class of nonlinear systems with unknown measurement sensitivity. A new design method, namely dual-domination approach, is proposed to explicitly construct a state observer as well as an output feedback control law, which globally asymptotically stabilizes the nonlinear systems. The novelty of this note owes to a distinct perspective in coping with unknown measurement sensitivity which has previously been a hurdle to solve the global output feedback stabilization problem of the nonlinear systems.