Multidimensional graphical method can be utilized on a multivariate data analysis through a procedure in which the multidimensional graphical method supports the statistical method with supplying deficiency of them.We present a procedure of combining both the face graph and Discriminant Function Method(DFM)to carry out exploratively discriminant analysis. However, in order to realize this procedure it needs to previously investigate differences of function between both methods.The results of the investigation showed that the face graph has two advantages over DFM that the discriminant analysis can be carried out when the training data are not sufficiently obtained and outliers in analysed data set can be easily found. Therefore, adopting the procedure of combining the face graph and DFM will make an efficient exploratory discriminant analysis.