Hermite subdivision schemes are particular vector subdivision schemes which produce function vectors consisting

of consecutive derivatives of a certain function. The convergence and smoothness of Hermite subdivision

schemes have been widely studied, while they are restricted in binary case. To ll this theoretical gap in the

literature, we study the convergence of Hermite subdivision schemes covering every arity, which can be seen as a

generalization of [7]. The convergence analysis is based on the connections among Hermite subdivision schemes,

vector subdivision schemes and renable function vectors. We provide a tool used to estimate the smoothness

of Hermite subdivision schemes of every arity by exploiting a quantity dened by sum rules and can construct

Hermite subdivision schemes of arbitrarily high smoothness from a convergent vector scheme of any arity.