  We introduce a notion of natural orderings of elements of finite connected
quandles of order $n$. When the elements of such a quandle $Q$ are already
ordered naturally, any automophism on $Q$ is a natural ordering. Although there
are many natural orderings, the operation tables for such orderings coincide
when the permutation $*q$ is a cycle of length $n-1$. This leads to the
classification of automorphisms on such a quandle. Moreover, it is also shown
that every row and column of the operation table of such a quandle contains all
the elements of $Q$, which is due to K. Oshiro. We also consider the general
case of finite connected quandles.
