A biconnected plane graph $G$ is called {\em internally
triconnected} if any cut-pair consists of
outer vertices and its removal results
in only components each of which contains at least one outer vertex. In a rooted plane graph, an edge is designated
as an outer edge with a specified direction.
For given positive integers $n\geq 1$ and $g\geq 3$,
let ${\cal G}_3(n,g)$ (resp., ${\cal G}_{\tt int}(n,g)$)
denote the class of all triconnected
(resp., internally triconnected)
rooted plane graphs with exactly
$n$ vertices such that the size of each inner face
is at most $g$.
In this paper, we present an efficient algorithm that enumerates
all rooted plane graphs in ${\cal G}_{\tt int}(n,g)-{\cal G}_3(n,g)$
in $O(n)$ space and in $O(1)$-time delay.