Four-dimensional variational assimilation (4D-Var) is a well-known retrospective analysis method. The minimization of the 4D-Var cost function is accomplished in general by using the adjoint model derived from the dynamic model for the assimilation. In order to implement 4D-Var differently from the conventional technique, in which the adjoint model is not required, we proposed a theory of retrospective optimal interpolation adopting a differential factor. We examined and confirmed the validity of our theory by consulting the results from the application of the theory to the three-variable Lorenz model.