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A difficult step in the process of karyotyping is segmenting chromosomes that touch or overlap. In an attempt to automate the process, previous studies turned to Deep Learning methods, with some formulating the task as a semantic segmentation problem. These models treat separate chromosome instances as semantic classes, which we show to be problematic, since it is uncertain which chromosome should be classed as #1 and #2. Assigning class labels based on comparison rules, such as the shorter/longer chromosome alleviates, but does not fully resolve the issue. Instead, we separate the chromosome instances in a second stage, predicting the orientation of the chromosomes by the model and use it as one of the key distinguishing factors of the chromosomes. We demonstrate this method to be effective. Furthermore, we introduce a novel Double-Angle representation that a neural network can use to predict the orientation. The representation maps any direction and its reverse to the same point. Lastly, we present a new expanded synthetic dataset, which is based on Pommier's dataset, but addresses its issues with insufficient separation between its training and testing sets.