Accurate detection of diabetic macular edema (DME) is an important task in optical coherence tomography (OCT) images of the eye. A relatively simple and practical approach is proposed in this paper. A pre-trained convolutional neural network (CNN) is fine tuned for a classification of DME versus normal cases. The fine-tuned Inception-Resnet-v2 CNN model can effectively identify pathologies in comparison to classical learning. Experiments were carried out on the publicly available data set of the Singapore Eye Research Institute (SERI). The developed model was also compared to other fine tuned models, such as Resnet-50 and Inception-v3. The proposed method achieved 100% classification accuracy with the Inception-Resnet-v2 model using a leave-one-out cross-validation strategy. For robustness, the model trained on the SERI dataset was tested on another dataset provided by the Chinese University HongKong (CUHK), also with 100% accuracy. The proposed method is a potentially impactful tool for accurately detecting DME vs. normal cases.