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The joint and relative effects of future land-use and climate change on fire occurrence in the Amazon, as well its seasonal variation, are still poorly understood, despite its recognized importance. Using the maximum entropy method (MaxEnt), we combined regional land-use projections and climatic data from the CMIP5 multimodel ensemble to investigate the monthly probability of fire occurrence in the mid (2041-2070) and late (2071-2100) 21st century in the Brazilian Amazon. We found striking spatial variation in the fire relative probability (FRP) change along the months, with October showing the highest overall change. Considering climate only, the area with FRP >= 0.3 (a threshold chosen based on the literature) in October increases 6.9% by 2071-2100 compared to the baseline period under the representative concentration pathway (RCP) 4.5 and 27.7% under the RCP 8.5. The best-case land-use scenario ("Sustainability") alone causes a 10.6% increase in the area with FRP >= 0.3, while the worse-case land-use scenario ("Fragmentation") causes a 73.2% increase. The optimistic climate-land-use projection (Sustainability and RCP 4.5) causes a 21.3% increase in the area with FRP >= 0.3 in October by 2071-2100 compared to the baseline period. In contrast, the most pessimistic climate-land-use projection (Fragmentation and RCP 8.5) causes a widespread increase in FRP (113.5% increase in the area with FRP >= 0.3), and prolongs the fire season, displacing its peak. Combining the Sustainability land-use and RCP 8.5 scenarios causes a 39.1% increase in the area with FRP >= 0.3. We conclude that avoiding the regress on land-use governance in the Brazilian Amazon (i.e., decrease in the extension and level of conservation of the protected areas, reduced environmental laws enforcement, extensive road paving, and increased deforestation) would substantially mitigate the effects of climate change on fire probability, even under the most pessimistic RCP 8.5 scenario.