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Next destination recommendation is an important task in the transportation domain of taxi and ride-hailing services, where users are recommended with personalized destinations given their current origin location. However, recent recommendation works do not satisfy this origin-awareness property, and only consider learning from historical destination locations, without origin information. Thus, the resulting approaches are unable to learn and predict origin-aware recommendations based on the user's current location, leading to sub-optimal performance and poor real-world practicality. Hence, in this work, we study the origin-aware next destination recommendation task. We propose the Spatial-Temporal Origin-Destination Personalized Preference Attention (STOD-PPA) encoder-decoder model to learn origin-origin (OO), destination-destination (DD), and origin-destination (OD) relationships by first encoding both origin and destination sequences with spatial and temporal factors in local and global views, then decoding them through personalized preference attention to predict the next destination. Experimental results on seven real-world user trajectory taxi datasets show that our model significantly outperforms baseline and state-of-the-art methods.