This paper presents a strategy of designing a trajectory-tracking control law for unmanned aerial vehicles where an unmodifiable autopilot is incorporated in the closed-loop system. The main contributions of this paper include a novel control structure that enables an explicit design of tracking methods for a system with an unmodifiable autopilot in the loop, and a novel controller that augments the existing control law. To begin with, a controller is developed based on a generalized design model using a Lyapunov-based backstepping technique. To incorporate the constraints due to the unmodifiable autopilot, the design model and the developed controller are augmented by introducing additional terms. Lyapunov stability theory is used to prove that, without any modification of the autopilot, the augmented controller exponentially stabilizes the vehicle to a desired trajectory while the other higher order and attitude states remain bounded. A software-in-the-loop simulation result is presented to validate the strategy. The proposed strategy can be employed to ensure the vehicle remains safe while experimenting with new tracking and path following control options. This type of control design are most useful for systems where the autopilot is unmodifiable, and possibly unknown, as would occur with commercial autopilots being augmented with high level tracking control.