NAVADAS-AR is a natural four-dimensional extension of NAVDAS (NRL Atmospheric Variational Data Assimilation System) where the AR stands for accelerated representer. In variational data assimilation, the smooth nonlinearity of atmospheric processes can usually be handled by the use of the outer iterations, where sequences of linear least-squares solutions converge to the non-linear one. Currently, most solution methods in atmospheric variational data assimilation use the incremental approach of Courtier et al. (1994), which enabled the operational implementation of a strong constraint (perfect model assumption) four-dimensional variational (4DVAR) data assimilation system at ECMWF. In this study, we mainly focus on the implementation and test of an outer loop procedure similar to the incremental approach in NAVDAS-AR. The results using this particular procedure will be presented. We will discuss the implications associated with the procedure and present an alternative iterative algorithm related to the Picard Iteration for the outer loop in NAVDAS-AR. To be presented at the Symposium on Forecasting the Weather and Climate of the Atmosphere and Ocean, 11-15 January 2004, Seattle, WA.