We propose a novel nonlinear control method for solving the problem of stabilization with guaranteed safety for nonlinear systems. The design is based on the merging of the well-known Control Lyapunov Function (CLF) and the recent concept of Control Barrier Function (CBF). The proposed control method allows us to combine the design of a stabilizing feedback law based on CLF and the design of safety control based on CBF(s); both of which can be designed independently. Our proposed approach can also accommodate the case of multiple CBFs which correspond to multiple different sets of unsafe states. Lastly, the efficacy of the proposed approach is demonstrated in the simulation results on the stabilization of a nonlinear mechanical system and on the navigation of a mobile robot.