This note investigates the fast tracking control problem of underactuated ships via persistent excitation (PE) conditions. By combining a novel transformation with the computed torque method, a decoupling controller related to the surge force is given first to decompose the error model into two cascade subsystems. Then, a stabilizing controller involving the yaw moment is designed. With the help of the proposed cascaded structure, a weaker PE condition than those given in past literature can be used to verify an integral detectability and guarantee global K-exponential convergence by employing several newly developed stability criteria. A new feature of the obtained results is that only one of these reference signals is needed to satisfy the usual PE condition. Simulation results are provided to validate the effectiveness of the proposed scheme.