The correlated data are of great importance in the practical life, for example we may want to track the case of a patient after taking a treatment for consecutive periods of time. Also, we may want to track a disease with the members of a certain family. Finally, we want to know the developement of a certain disease with a patient for different periods of time, … , etc. the binary data, (for example a person smokes = 1, a person does not smoke = 0), (female = 1, male = 0), (the effect of treatment is active =1, placebo = 0), is a type of the correlated data. In this paper, we are applying the classification and discriminant methods  on the correlated data (some of them are binary data and the other are not). Usually we are using a one dependent variable and then we classify it into two or more classes. Contrary to what is traditionally followed, in this paper we will deal with two dependent correlated categorical variables each one is divided into two classes. The methods of discriminant analysis are investigated in this paper when we are dealing with the independent and dependent variables both of them is correlated variables.