The descending palatine artery branches off of the maxillary artery in the pterygopalatine fossa and descends through the greater palatine canal along with the greater palatine nerve (from the pterygopalatine ganglion).
A branch of the maxillary artery, the descending palatine artery originates in the pterygopalatine fossa and travels down the greater palatine canal with the accompanying greater palatine nerve from the pterygopalatine ganglion.