Data used by automated decision-making systems, such as Machine Learning models, often reflects discriminatory behavior that occurred in the past. These biases in the training data are sometimes related to label noise, such as in COMPAS, where more African-American offenders are wrongly labeled as having a higher risk of recidivism when compared to their White counterparts. Models trained on such biased data may perpetuate or even aggravate the biases with respect to sensitive information, such as gender, race, or age. However, while multiple label noise correction approaches are available in the literature, these focus on model performance exclusively. In this work, we propose Fair-OBNC, a label noise correction method with fairness considerations, to produce training datasets with measurable demographic parity. The presented method adapts Ordering-Based Noise Correction, with an adjusted criterion of ordering, based both on the margin of error of an ensemble, and the potential increase in the observed demographic parity of the dataset. We evaluate Fair-OBNC against other different pre-processing techniques, under different scenarios of controlled label noise. Our results show that the proposed method is the overall better alternative within the pool of label correction methods, being capable of attaining better reconstructions of the original labels. Models trained in the corrected data have an increase, on average, of 150% in demographic parity, when compared to models trained in data with noisy labels, across the considered levels of label noise.