Euclidean word embedding models such as GloVe and Word2Vec have been shown to reflect human-like gender biases. In this paper, we extend the study of gender bias to the recently popularized hyperbolic word embeddings. We propose gyrocosine bias, a novel measure for quantifying gender bias in hyperbolic word representations and observe a significant presence of gender bias. To address this problem, we propose Poincar\é Gender Debias (PGD), a novel debiasing procedure for hyperbolic word representations. Experiments on a suit of evaluation tests show that PGD effectively reduces bias while adding a minimal semantic offset.
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