  A proper $k$-coloring of $G$ is called an odd coloring of $G$ if for every
vertex $v$, there is a color that appears at an odd number of neighbors of $v$.
This concept was introduced recently by Petru\v{s}evski and \v{S}krekovski, and
they conjectured that every planar graph is odd 5-colorable. Towards this
conjecture, Caro, Petru\v{s}evski, and \v{S}krekovski showed that every
outerplanar graph is odd 5-colorable, and this bound is tight since the cycle
of length 5 is not odd 4-colorable. Recently, the first author and others
showed that every maximal outerplanar graph is odd 4-colorable. In this paper,
we show that a connected outerplanar graph $G$ is odd 4-colorable if and only
if $G$ contains a block which is not a copy of the cycle of length 5. This
strengthens the result by Caro, Petru\v{s}evski, and \v{S}krekovski, and gives
a complete characterization of odd 4-colorable outerplanar graphs.
