The authors propose a new two-step algorithm for discrete nonlinear systems which avoids linearizing the quadratic cost function by splitting the minimization into two parts. The linear first-step problem is solved by use of the Kalman filter while the nonlinear second-step problem is solved via an iterative Gauss-Newton algorithm. In the static state situation, optimality is proved when the time variation of the system can be separated from the unknowns. Under suitable assumptions, optimality is also established in the dynamic state situation. An analytical comparison is made in which the extended and iterated extended Kalman filters are shown to be both biased and suboptimal. Finally, two illustrative examples are provided.