Transformer attention architectures, similar to those developed for natural language processing, have recently proved efficient also in vision, either in conjunction with or as a replacement for convolutional layers. Typically, visual attention is inserted in the network architecture as a (series of) feedforward self-attention module(s), with mutual key-query agreement as the main selection and routing operation. However efficient, this strategy is only vaguely compatible with the way that attention is implemented in biological brains: as a separate and unified network of attentional selection regions, receiving inputs from and exerting modulatory influence on the entire hierarchy of visual regions. Here, we report experiments with a simple such attention system that can improve the performance of standard convolutional networks, with relatively few additional parameters. Each spatial position in each layer of the network produces a key-query vector pair; all queries are then pooled into a global attention query. On the next iteration, the match between each key and the global attention query modulates the network's activations -- emphasizing or silencing the locations that agree or disagree (respectively) with the global attention system. We demonstrate the usefulness of this brain-inspired Global Attention Agreement network (GAttANet) for various convolutional backbones (from a simple 5-layer toy model to a standard ResNet50 architecture) and datasets (CIFAR10, CIFAR100, Imagenet-1k). Each time, our global attention system improves accuracy over the corresponding baseline.