The sample cross-correlation function (SCCF) has been used to study the strength and direction of the linear relation between two jointly stationary stochastic processes. Rosales (2004) and Castano (2005) show that the cross-correlation function between a stationary process and the residuals of an estimated preliminary model can be used as an additional diagnostic tool, for the identification of an appropriate ARMA(p, q) model, for the generating process of the series. The purpose of this article is to show that the FCCM between a series and the residual of a preliminary model to describe it, not necessarily correct, contains relevant information of the correct model and for this reason it can be used as a diagnostic tool for the construction of ARMA models. The procedure is ilustrated with real and simulated series.