We are considering non-linear system identification based on the Hammerstein model i.e. a non-linear static gain in series with linear dynamics. The static gain characteristic is any non-linear function F. An identi. cation scheme is designed to get estimates of both the plant dynamics model and a set of N different points (x, F(x)), where N is arbitrarily chosen by the user. Such a scheme involves least squares and prediction-error algorithms as well as algebraic transformations such as singular values decomposition (SVD). Interestingly, the proposed scheme ensures persistent excitation allowing thus exact model identi. cation in the case of no external disturbances.