Detecting tiny objects is a fundamental task in computer vision but poses a considerable challenge for existing detectors. One issue is that task-irrelevant objects or non-object background patches can be mistakenly detected as objects of interest, significantly impairing detector precision. To tackle this issue we propose an online image augmentation technique, NegCopyPaste, in the training process. This method copies regions of training images falsely identified as target objects in one epoch and pastes them into the training images for the next epoch. By training the model to reject false-positive predictions made in previous epochs, the proposed method effectively decreases the proportion of false-positive predictions compared to the baselines, making the network more selective in picking out the target objects. NegCopyPaste reduces the number of false-positive predictions during inference and achieves new state-of-the-art results on TinyPerson, WiderFace and DOTA, notably improving \(mAP_{tiny}\) by 1.58% over the previous best method on TinyPerson.