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Glaucoma is an intricate sickness that is caused due to the damage of optic nerve. It is the second foremost reason for the loss of sight. To diagnose glaucoma, Tripartite Tier Convolutional Neural Network Scheme (TT_CNN Scheme) was proposed. TT_CNN Scheme comprises three tiers namely top tier, middle tier and bottom tier. Each tier contains hidden layers such as convolution, relu, max pooling, drop out and fully connected layer. The input retinal images are processed through the hidden layers and the obtained outputs are concatenated and classified as normal or glaucomatous. Support vector machine classifier, K-Nearest Neighbour classifier, Random Forest Classifier, Decision tree classifier are used to classify the processed retinal images as healthy or glaucomatous images. Amongst the classifiers, Random Forest Classifier exemplifies better performance than other classifiers. This TT_CNN Scheme has been analysed using MIAG RIMONE (Release2) database and MIAG RIMONE (Release3) database. The performance metrics illustrates enhanced results for TT_CNN Scheme than single tier CNN method. This TT_CNN Scheme achieves a sensitivity of 99.26% and 98.6 % in classifying glaucoma images for MIAG RIMONE (Release2) database and MIAG RIMONE (Release3) database respectively. This Scheme also produces an overall accuracy of 99.26% and 99.1% using Random Forest Classifier for MIAG RIMONE (Release 2) database and MIAG RIMONE (Release3) database correspondingly.