  For a continuous action $G\curvearrowright X$ of a countable group on a
compact metrizable space we show that the following are equivalent: (i) the
action $G\curvearrowright X$ has the small boundary property and no finite
orbits, (ii) for every continuous action $H\curvearrowright Y$ of a countable
group on a compact metrizable space, the product action $G\times
H\curvearrowright X\times Y$ has the small boundary property. In particular,
(ii) is automatic when $G$ is infinite and the action $G\curvearrowright X$ is
minimal and has the small boundary property. The argument relies on a small
boundary version of the Urysohn lemma.
