  This paper presents full classification of second minimal odd periodic orbits
of a continuous endomorphisms on the real line. A $(2k+1)$-periodic orbit
($k\geq 3$) is called second minimal for the map $f$, if $2k-1$ is a minimal
period of $f$ in the Sharkovskii ordering. We prove that there are $4k-3$ types
of second minimal $(2k+1)$-orbits, each characterized with unique cyclic
permutation and directed graph of transitions with accuracy up to inverses.
