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In the past decade, deep neural networks, and specifically convolutional neural networks (CNNs), have been becoming a primary tool in the field of biomedical image analysis, and are used intensively in other fields such as object or face recognition. CNNs have a clear advantage in their ability to provide superior performance, yet without the requirement to fully understand the image elements that reflect the biomedical problem at hand, and without designing specific algorithms for that task. The availability of easy-to-use libraries and their non-parametric nature make CNN the most common solution to problems that require automatic biomedical image analysis. But while CNNs have many advantages, they also have certain downsides. The features determined by CNNs are complex and unintuitive, and therefore CNNs often work as a “Black Box”. Additionally, CNNs learn from any piece of information in the pixel data that can provide a discriminative signal, making it more difficult to control what the CNN actually learns. Here we follow common practices to test whether CNNs can classify biomedical image datasets, but instead of using the entire image we use merely parts of the images that do not have biomedical content. The experiments show that CNNs can provide high classification accuracy even when they are trained with datasets that do not contain any biomedical information, or can be systematically biased by irrelevant information in the image data. The presence of such consistent irrelevant data is difficult to identify, and can therefore lead to biased experimental results. Possible solutions to this downside of CNNs can be control experiments, as well as other protective practices to validate the results and avoid biased conclusions based on CNN-generated annotations.