Starting from and examination of the confusing names and concepts currently used for the so-called shuzi gua or numerical allograms, this article reconsiders several fundamental issues in the early numerical divinatory material. Supported by extensive evidence form recent archaeological discoveries, this author argues that (1) although the numerical allograms are related to the Zhouyi or the Book of Changes, they are not necessarily the trigrams or hexagrams of the Zhouyi since the Zhouyi is not the only divinatory system in early China; (2) the numerical allograms could be either actual numbers obtained from early divinatory practices or allogram pictures representing those numbers; (3) the numerical allograms reflect a multivariate and immature development of early Chinese divination thus both greatly enrich our knowledge of early Chinese divination and request our further research on its various sub-traditions; (4) some numerical allograms provide evidence supporting the theory of duel trigrams, chonggua, on the formation of the sixty-four hexagrams of the Zhouyi; (5) the numerical allogram material may provide clues for both the origins of allogram names, including early hexagram names of the Zhouyi, and the examination of different numerical allogram subsystems; and (6) the evidence of inverted hexagrams, fugua, in the numerical allograms is critical to the understanding of the relationship between the numerical allograms and the Zhouyi; in particular, if the inverted hexagrams of the numerical hexagrams originated from the Zhouyi or the early forms of the Zhouyi, it would seriously challenge the conventional understandings of the data and composition of the Zhouyi, the nature of the numerical allograms and a series of important issues in the field.