The Uda school traces its origin to the late Kamakura period, when the elder priest Konyudo Kunimitsu relocated from Uda District in Yamato Province to Etchu Province, thereby becoming the founder of the lineage. Kunimitsu's sons included Kunifusa and Kunimune, and the line prospered through the Nanbokucho period and onward into the Muromachi period. Works from the late Kamakura through the Nanbokucho period are generally referred to as Ko-Uda. Among blades signed Kunimitsu, there appear to have been multiple generations, with smiths succeeding to the same name into the Muromachi period.

Since the Uda group originally came from Yamato Province, their works naturally tend to show strong Yamato characteristics. The jigane displays itame mixed with mokume, with chikei appearing and well-developed ji-nie; the steel often shows a golden tone with some blackish coloration, becoming whitish in places. Early Ko-Uda works exhibit strong koshizori with funbari and ko-kissaki, while the later Oei-era Kunimitsu produces refined, slender tanto in hira-zukuri with uchizori. The hamon ranges from shallow notare-based gunome-midare with deep nioi and well-adhering nie to narrow suguha carrying a slight ko-notare and fine hotsure. The boshi in o-maru with a tendency toward yakitsume conveys the school's Yamato provenance.

Both the Ko-Uda founder's works and the later Oei-era Kunimitsu are consistently praised as kenzen and of notably high workmanship. The distinctive blackish cast within the golden-toned jigane and the presence of rounded nie within the temper are hallmarks by which the school's characteristics are clearly indicated. The earliest dated work, bearing a Gen'o 3 (1321) inscription, constitutes valuable documentary material for the study of the school's origins.