Breast cancer is the second most frequent cancer worldwide, following lung cancer and the fifth leading cause of cancer death and a major cause of cancer death among women. In recent years, convolutional neural networks (CNNs) have been successfully applied for the diagnosis of breast cancer using different imaging modalities. Pooling is a main data processing step in CNN that decreases the feature maps' dimensionality without losing major patterns. However, the effect of pooling layer was not studied efficiently in literature. In this paper, we propose a novel design for the pooling layer called vector pooling block (VPB) for the CCN algorithm. The proposed VPB consists of two data pathways, which focus on extracting features along horizontal and vertical orientations. The VPB makes the CNNs able to collect both global and local features by including long and narrow pooling kernels, which is different from the traditional pooling layer, that gathers features from a fixed square kernel. Based on the novel VPB, we proposed a new pooling module called AVG-MAX VPB. It can collect informative features by using two types of pooling techniques, maximum and average pooling. The VPB and the AVG-MAX VPB are plugged into the backbone CNNs networks, such as U-Net, AlexNet, ResNet18 and GoogleNet, to show the advantages in segmentation and classification tasks associated with breast cancer diagnosis from thermograms. The proposed pooling layer was evaluated using a benchmark thermogram database (DMR-IR) and its results compared with U-Net results which was used as base results. The U-Net results were as follows: global accuracy = 96.6%, mean accuracy = 96.5%, mean IoU = 92.07%, and mean BF score = 78.34%. The VBP-based results were as follows: global accuracy = 98.3%, mean accuracy = 97.9%, mean IoU = 95.87%, and mean BF score = 88.68% while the AVG-MAX VPB-based results were as follows: global accuracy = 99.2%, mean accuracy = 98.97%, mean IoU = 98.03%, and mean BF score = 94.29%. Other network architectures also demonstrate superior improvement considering the use of VPB and AVG-MAX VPB.