This paper presents a new control law for the problem of coordinated path following. The paper deals with a group of car like vehicles, where each vehicle is represented by the bicycle kinematic model. A nonlinear control law has been designed by the Lyapunov approach. The Lyapunov function includes the position errors of all vehicles with respect to the desired paths, and the coordination errors that describe deviations from the reference geometric formation. The time derivative of the path parameter is utilized as an additional control input that synchronizes between vehicles. The main contribution of this paper stems from the inclusion of the bicycle kinematic model in the development (and not only the unicycle model as in earlier works) that is more complex due to its two nonholonomic constraints. The stability of the coordinated path following controller is proven and its effectiveness is demonstrated using numerical simulations.