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The monophyly of the trilobite Order Asaphida has been challenged. The Superfamily Remopleuridioidea was included in the Order Asaphida, based on the ventral median suture and highly bulbous protaspis of the late Furongian–Tremadocian representatives of the group. The remopleuridioid, Haniwa quadrata Kobayashi, 1933 from the Furongian (late Cambrian) Hwajeol Formation of Korea, represents a primitive morphology of the Remopleuridioidea. This trilobite does not have a typical globular morphology of asaphoid protaspis, and the free cheeks remained yoked together during the whole of the development. This supports the previous proposition that the Superfamily Remopleuridioidea should be excluded from the Order Asaphida. In addition, the evolution of a highly globular protaspis of the Ordovician remopleuridioid trilobites from the less bulbous protaspis corroborates the possibility of multiple evolutions of a highly globular protaspis. It can be argued that the possession of a highly globular protaspis does not guarantee the membership of the Order Asaphida, and thus the concept of the Order Asaphida should be emended.