In this paper, we propose a new asymptotically stabilizing control law for a four-wheeled vehicle with a steering limitation. We adopt a locally semiconcave control Lyapunov function (LS-CLF) for the system. To overcome the nonconvexity of the input-constraint set, we utilize a saturation function and a signum function in the control law. The signum function makes the vehicle velocity nonzero except at the origin so that the angular velocity can be manipulated within the input constraint. However, the signum function may cause a chattering phenomenon at certain points of the state far from the origin. Thus, we integrate a lazy-switching mechanism for the vehicle velocity into the control law. The mechanism makes a sign of the vehicle velocity maintain, and the new control input also decreases the value of the LS-CLF. We confirm the effectiveness of our method by a computer simulation and experiments.