Quadratic discriminant analysis is a well-established supervised classification method, which extends the linear discriminant analysis by relaxing the assumption of equal covariances across classes. In this study, assuming known but not equal covariance matrices for the classes, a quadratic classification rule based on repeated measurements is developed. We employ a bilinear regression model to assign new observations to predefined populations and approximate the misclassification probabilities using an Edgeworth-type expansion. Through weighted estimators, we estimate unknown mean parameters and derive moments of the quadratic classifier. We then conduct numerical simulations to compare misclassification probabilities using true and estimated mean parameters, as well as misclassification probabilities computed through Monte Carlo simulations. Our findings suggest that as the distance between groups widens, the misclassification probability curve decreases, indicating that classifying observations is easier in widely separated groups compared to closely clustered ones.