Due to the difficulty in solving the Hamilton-Jacobi-Isaacs equation, the nonlinear optimal control approach is not very practical in general. To overcome this problem, Ezal et al. (2000) first solved a linear optimal control problem for the linearized model of a nonlinear system given in the strict-feedback form. Then, using the backstepping procedure, a nonlinear feedback controller was designed where the linear part is same as the linear feedback obtained from the linear optimal control design. However, their construction is based on the cancellation of the high order nonlinearity, which limits the application to the smooth ($C^{infty}$) vector fields. In this paper, we develop an alternative method for backstepping procedure, so that the vector field can be just $C^1$, which allows this approach to be applicable to much larger class of nonlinear systems.