  Let $K$ be a global function field together with a place $\infty$, and $A$
the subring of functions regular outside $\infty$. In this paper we present an
effective method to evaluate the (locally free) class number of an arbitrary
hereditary $A$-order in an arbitrary definite central simple $K$-algebra. We
also show that the class number of any non-principal genus for a hereditary
order in $D$ can be reduced to that of the principal genus for another
hereditary order in $D$.
