The Oki Islands, Shimane Prefecture, are considered the only area which has three-pattern accentuation in Mainland Japan, although it has been reported that several dialects of the Ryukyuan language have three-pattern accentuation. However, I have discovered three-pattern accentuation also exists in the Kokonogi dialect, Fukui Prefecture, which is located east of the Oki Islands. This paper will first describe the accent system of this dialect and verify that the dialect has some of the characteristics peculiar to N-pattern accent systems. However, the dialect does not have consistency of accent pattern in forms of the verb conjugation, something observed in some dialects with an N-pattern accent system. Finally, I will try to give a historical reason for this inconsistency by showing the correspondences between the verbal accentuation of the Kokonogi dialect and those of the Kochi dialect, which retains older accent forms than the Kyoto dialect.